Paul Seymour | Academic Influence

Paul Seymour 's AcademicInfluence.com Rankings

Paul Seymour

Mathematics

#167

World Rank

#396

Historical Rank

Graph Theory

#9

World Rank

#13

Historical Rank

Measure Theory

#379

World Rank

#558

Historical Rank

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Mathematics

Paul Seymour 's Degrees

PhD Mathematics Princeton University

Why Is Paul Seymour Influential?

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According to Wikipedia, Paul D. Seymour is a British mathematician known for his work in discrete mathematics, especially graph theory. He was responsible for important progress on regular matroids and totally unimodular matrices, the four colour theorem, linkless embeddings, graph minors and structure, the perfect graph conjecture, the Hadwiger conjecture, claw-free graphs, χ-boundedness, and the Erdős–Hajnal conjecture. Many of his recent papers are available from his website.

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Paul Seymour 's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Graph Minors. II. Algorithmic Aspects of Tree-Width (1986) (1633)
Graph Minors .XIII. The Disjoint Paths Problem (1995) (1255)
Graph Minors (2009) (1168)
Graph Minors. XX. Wagner's conjecture (2004) (885)
Graph minors. III. Planar tree-width (1984) (755)
Graph Minors: XV. Giant Steps (1996) (749)
Graph minors. V. Excluding a planar graph (1986) (742)
Decomposition of regular matroids (1980) (716)
Graph minors. X. Obstructions to tree-decomposition (1991) (713)
The Complexity of Multiterminal Cuts (1994) (653)
The Four-Colour Theorem (1997) (606)
The Strong Perfect Graph Theorem (2002) (598)
Graph minors. I. Excluding a forest (1983) (584)
Approximating clique-width and branch-width (2006) (468)
Quickly Excluding a Planar Graph (1994) (444)
Graph Searching and a Min-Max Theorem for Tree-Width (1993) (411)
Call routing and the ratcatcher (1994) (334)
Graph Minors. XVI. Excluding a non-planar graph (2003) (334)
Recognizing Berge Graphs (2005) (311)
Hadwiger's conjecture forK6-free graphs (1993) (288)
Directed Tree-Width (2001) (277)
Nowhere-zero 6-flows (1981) (251)
Monotonicity in Graph Searching (1991) (251)
Disjoint paths in graphs (2006) (247)
Percolation probabilities on the square lattice (1978) (243)
PERMANENTS, PFAFFIAN ORIENTATIONS, AND EVEN DIRECTED CIRCUITS (1999) (240)
On Multi‐Colourings of Cubic Graphs, and Conjectures of Fulkerson and Tutte (1979) (235)
The complexity of multiway cuts (extended abstract) (1992) (233)
The matroids with the max-flow min-cut property (1977) (233)
Averaging sets: A generalization of mean values and spherical designs (1984) (219)
Packing directed circuits fractionally (1995) (219)
A separator theorem for nonplanar graphs (1990) (213)
A separator theorem for graphs with an excluded minor and its applications (1990) (213)
The structure of claw-free graphs (2005) (206)
Graph minors. IV. Tree-width and well-quasi-ordering (1990) (203)
Sachs' Linkless Embedding Conjecture (1995) (199)
Tour Merging via Branch-Decomposition (2003) (195)
The roots of the independence polynomial of a clawfree graph (2007) (185)
Graph minors. VII. Disjoint paths on a surface (1988) (168)
Packing directed circuits (1996) (167)
Surveys in combinatorics 1985: Graph minors – a survey (1985) (164)
Multicommodity flows in planar graphs (1981) (160)
A new proof of the four-colour theorem (1996) (159)
The Ring Loading Problem (1998) (158)
Graph minors. VIII. A kuratowski theorem for general surfaces (1990) (151)
Matroids and Multicommodity Flows (1981) (150)
Spanning trees with many leaves (2001) (148)
Graph minors XXIII. Nash-Williams' immersion conjecture (2010) (141)
On Odd Cuts and Plane Multicommodity Flows (1981) (138)
Efficiently four-coloring planar graphs (1996) (115)
Quickly excluding a forest (1991) (115)
Graph minors. IX. Disjoint crossed paths (1990) (113)
Matroid representation over GF(3) (1979) (113)
A survey of χ ‐boundedness (2020) (107)
Excluding any graph as a minor allows a low tree-width 2-coloring (2004) (105)
Graph minors. VI. Disjoint paths across a disc (1986) (104)
Claw-free graphs. V. Global structure (2008) (104)
Planar Separators (1994) (101)
On secret-sharing matroids (1992) (98)
Graph Minors. XI. Circuits on a Surface (1994) (97)
The Structure of Homometric Sets (1982) (92)
The metamathematics of the graph minor theorem (1985) (88)
Proper minor-closed families are small (2006) (82)
The Forbidden Minors of Binary Clutters (1976) (76)
Hadwiger's Conjecture (2016) (76)
Recognizing graphic matroids (1981) (76)
ON THE TWO-COLOURING OF HYPERGRAPHS (1974) (73)
On induced subgraphs of the cube (1988) (71)
Claw-free graphs. IV. Decomposition theorem (2008) (71)
On the odd-minor variant of Hadwiger's conjecture (2009) (69)
Induced subgraphs of graphs with large chromatic number. I. Odd holes (2014) (69)
Packing Non-Zero A-Paths In Group-Labelled Graphs (2006) (69)
Graphs with small bandwidth and cutwidth (1989) (68)
The three-in-a-tree problem (2010) (66)
Graph Minors .XII. Distance on a Surface (1995) (65)
Linkless embeddings of graphs in 3-space (1993) (65)
Disjoint Paths—A Survey (1985) (65)
A note on the production of matroid minors (1977) (63)
Characterization of even directed graphs (1987) (62)
Bisimplicial vertices in even-hole-free graphs (2008) (62)
Graph Minors: XVII. Taming a Vortex (1999) (62)
On minors of non-binary matroids (1981) (60)
A survey of linkless embeddings (1991) (60)
Excluding induced subgraphs (2006) (59)
Tutte's Edge-Colouring Conjecture (1997) (59)
Progress on perfect graphs (2003) (57)
Combinatorial applications of an inequality from statistical mechanics (1975) (57)
Claw-free graphs. III. Circular interval graphs (2008) (56)
Finding disjoint trees in planar graphs in linear time (1991) (55)
Graphs of bounded rank-width (2005) (54)
Excluding a graph with one crossing (1991) (54)
Tournaments and colouring (2012) (53)
Graph minors. XXI. Graphs with unique linkages (2009) (53)
On the fractional matching polytope of a hypergraph (1993) (53)
On Tutte's extension of the four-colour problem (1981) (52)
Graph Minors. XXII. Irrelevant vertices in linkage problems (2012) (51)
Detecting even holes (2005) (51)
Large induced degenerate subgraphs (1987) (49)
Claw-free graphs. I. Orientable prismatic graphs (2007) (48)
Induced subgraphs of graphs with large chromatic number. XIII. New brooms (2018) (47)
Bounding the vertex cover number of a hypergraph (1994) (47)
Minors of 3-Connected Matroids (1985) (47)
Self-organizing sequential search and Hilbert's inequalities (1985) (46)
A well-quasi-order for tournaments (2011) (45)
A FORBIDDEN MINOR CHARACTERIZATION OF MATROID PORTS (1976) (45)
On Lehman's Width-Length Characterization (1990) (45)
Fractional Colouring and Hadwiger's Conjecture (1998) (45)
Claw-free graphs. II. Non-orientable prismatic graphs (2008) (44)
Testing branch-width (2007) (42)
Graph Structure Theory, Proceedings of a AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors held June 22 to July 5, 1991, at the University of Washington, Seattle, USA (1993) (42)
Graph Minors. XIX. Well-quasi-ordering on a surface (2004) (41)
A counterexample to the rank-coloring conjecture (1989) (41)
Permanents, Pfaffian orientations, and even directed circuits (extended abstract) (1997) (41)
Colouring series-parallel graphs (1990) (40)
A simpler proof and a generalization of the zero-trees theorem (1991) (40)
Claw-free graphs VI. Colouring (2010) (39)
Tree-width and planar minors (2015) (39)
Analyzing the Performance of Greedy Maximal Scheduling via Local Pooling and Graph Theory (2012) (39)
K4-free graphs with no odd holes (2010) (39)
Induced Subgraphs of Graphs with Large Chromatic Number. III. Long Holes (2015) (39)
Cycles in dense digraphs (2007) (38)
Hadwiger's conjecture for line graphs (2004) (37)
Coloring Locally Bipartite Graphs on Surfaces (2002) (37)
Matroid minors (1996) (37)
Colouring Eulerian Triangulations (2002) (35)
Four-terminus flows (1980) (34)
Extending an edge-coloring (1990) (34)
The edge-density for K2, t minors (2011) (34)
A short proof of the two-commodity flow theorem (1979) (33)
A counterexample to a conjecture of Schwartz (2013) (32)
Tournament immersion and cutwidth (2012) (32)
Claw-free graphs. VII. Quasi-line graphs (2012) (32)
A Relative of Hadwiger's Conjecture (2014) (31)
Induced Subgraphs of Graphs with Large Chromatic Number IX: Rainbow Paths (2017) (31)
Packing circuits in eulerian digraphs (1996) (31)
Induced subgraphs of graphs with large chromatic number. VIII. Long odd holes (2017) (31)
Induced Subgraphs of Graphs With Large Chromatic Number. X. Holes of Specific Residue (2017) (29)
Induced subgraphs of graphs with large chromatic number. XII. Distant stars (2017) (29)
Even circuits in planar graphs (1981) (28)
Perfect matchings in planar cubic graphs (2012) (28)
Disjoint paths in tournaments (2014) (28)
Edge-disjoint paths in digraphs with bounded independence number (2015) (27)
An end-faithful spanning tree counterexample (1991) (26)
Graph Minors .XIV. Extending an Embedding (1995) (26)
Excluding infinite minors (1991) (25)
A fractional version of the Erdős-Faber-Lovász conjecture (1992) (25)
A Note on Hyperplane Generation (1994) (25)
Tournament minors (2012) (25)
Induced subgraphs of graphs with large chromatic number. IV. Consecutive holes (2015) (25)
A two-commodity cut theorem (1978) (24)
Even pairs in Berge graphs (2009) (24)
Pure pairs. I. Trees and linear anticomplete pairs (2018) (24)
Large rainbow matchings in general graphs (2016) (24)
Disjoint Paths in a Planar Graph - A General Theorem (1992) (24)
On incomparable collections of sets (1973) (23)
Graph Minors. XVIII. Tree-decompositions and well-quasi-ordering (2003) (22)
Detecting an Odd Hole (2019) (22)
Induced subgraphs of bounded treewidth and the container method (2020) (22)
Petersen Family Minors (1995) (22)
Extending the Gyárfás-Sumner conjecture (2014) (22)
On the points-lines-planes conjecture (1982) (21)
Irreducible Triangulations of Surfaces (1996) (21)
Triples in Matroid Circuits (1986) (21)
Circular embeddings of planar graphs in nonspherical surfaces (1994) (21)
Caterpillars in Erdős-Hajnal (2019) (21)
Edge-colouring eight-regular planar graphs (2012) (20)
Excluding subdivisions of infinite cliques (1992) (20)
On forbidden minors for (3) (1988) (20)
A Note on List Arboricity (1998) (19)
Excluding paths and antipaths (2015) (19)
A note on a combinatorial problem of Erdős and Hajnal (1974) (19)
Uniqueness of highly representative surface embeddings (1996) (19)
Subgraphs of large connectivity and chromatic number in graphs of large chromatic number (1987) (19)
Tournament pathwidth and topological containment (2013) (19)
Packing nearly-disjoint sets (1982) (18)
How the proof of the strong perfect graph conjecture was found (2006) (18)
Some New Results on the Well-Quasi-Ordering of Graphs (1984) (18)
Packing seagulls (2012) (18)
Adjacency in Binary Matroids (1986) (18)
Rao's degree sequence conjecture (2014) (17)
Induced subgraphs of graphs with large chromatic number. II. Three steps towards Gyárfás' conjectures (2014) (17)
Towards Erdős-Hajnal for Graphs with No 5-Hole (2018) (17)
Clustered Colouring in Minor-Closed Classes (2017) (17)
A survey of $\chi$-boundedness (2018) (17)
Kuratowski Chains (1995) (16)
Induced subgraphs of graphs with large chromatic number. V. Chandeliers and strings (2016) (15)
Excluding Infinite Clique Minors (1995) (15)
Tournaments with near-linear transitive subsets (2014) (15)
Induced subgraphs of graphs with large chromatic number. XI. Orientations (2017) (14)
Spanning Trees of Different Weights (1990) (14)
Unavoidable induced subgraphs in large graphs with no homogeneous sets (2015) (14)
Induced subgraphs of graphs with large chromatic number. VI. Banana trees (2017) (14)
Three-edge-colouring doublecross cubic graphs (2014) (13)
Cyclically five-connected cubic graphs (2015) (13)
Packing and covering with matroid circuits (1980) (13)
Node Placement and Sizing for Copper Broadband Access Networks (2001) (13)
On the connectivity function of a matroid (1987) (13)
Proof of the Kalai-Meshulam conjecture (2018) (13)
Non-Planar Extensions Of Planar Graphs (1999) (13)
A Local Strengthening of Reed's Omega, Delta, Chi Conjecture for Quasi-line Graphs (2011) (12)
Extending partial 3-colourings in a planar graph (2003) (12)
Packing Odd Paths (1994) (12)
Edge-colouring seven-regular planar graphs (2012) (12)
Trees and linear anticomplete pairs (2018) (12)
A generalization of chordal graphs (1984) (12)
Directed circuits on a torus (1991) (12)
Induced subgraphs of graphs with large chromatic number. VII. Gyárfás' complementation conjecture (2017) (12)
On Tutte's Characterization of Graphic Matroids (1980) (12)
Pure Pairs. II. Excluding All Subdivisions of A Graph (2020) (11)
A proof of total dual integrality of matching polyhedra (1977) (11)
Growing Without Cloning (2012) (11)
Even-hole-free graphs still have bisimplicial vertices (2019) (11)
Tree-chromatic number (2016) (11)
A note on nongraphic matroids (1984) (10)
Two Chromatic Polynomial Conjectures (1997) (10)
Eulerian digraph immersion (2002) (10)
Majority Colourings of Digraphs (2016) (10)
Detecting Matroid Minors (1981) (10)
The smallestn-uniform hypergraph with positive discrepancy (1987) (10)
Detecting an induced net subdivision (2013) (10)
Excluding A Grid Minor In Planar Digraphs (2015) (10)
Excluding pairs of graphs (2013) (10)
Polynomial bounds for chromatic number. IV. A near-polynomial bound for excluding the five-vertex path (2021) (10)
Polynomial bounds for chromatic number. I. Excluding a biclique and an induced tree (2021) (10)
Sparse graphs without linear anticomplete pairs (2018) (9)
Excluded minors in cubic graphs (2014) (9)
Rooted grid minors (2013) (9)
Excluding infinite trees (1993) (9)
Immersion in four-edge-connected graphs (2013) (8)
Colouring graphs with no odd holes (2014) (8)
Disjoint paths in unions of tournaments (2016) (8)
Finding an induced path that is not a shortest path (2020) (8)
Polynomial bounds for chromatic number. III. Excluding a double star (2021) (8)
Analyzing the performance of greedy maximal scheduling via local pooling and graph theory (2010) (8)
Colouring perfect graphs with bounded clique number (2017) (7)
Counting points in hypercubes and convolution measure algebras (1985) (7)
Polynomial bounds for chromatic number II: Excluding a star‐forest (2021) (7)
Testing for a theta (2007) (6)
quasi-line graphs (2011) (6)
Progress on the Four-Color Theorem (1995) (6)
Pure pairs. VII. Homogeneous submatrices in 0/1-matrices with a forbidden submatrix (2021) (6)
Pure pairs. III. Sparse graphs with no polynomial‐sized anticomplete pairs (2018) (6)
Three-colourable perfect graphs without even pairs (2012) (6)
Detecting a Long Odd Hole (2019) (6)
Certifying large branch-width (2006) (6)
Domination in tournaments (2017) (6)
Disjoint Cycles in Directed Graphs on the Torus and the Klein Bottle (1993) (6)
Wheel-free planar graphs (2013) (6)
Finding a Shortest Odd Hole (2020) (6)
Pure Pairs VI: Excluding an Ordered Tree (2020) (6)
Detecting a long even hole (2020) (5)
Bipartite minors (2013) (5)
A Petersen on a Pentagon (1998) (5)
Forbidden structures and algorithms in graphs and digraphs (2011) (5)
Pure pairs. VIII. Excluding a sparse graph (2022) (5)
Criticality for multicommodity flows (2015) (5)
Proof of a conjecture of Plummer and Zha (2022) (5)
Tutte's Three-Edge-Colouring Conjecture (2012) (5)
Long cycles in critical graphs (2000) (5)
Triangle-free graphs with no six-vertex induced path (2018) (5)
Strengthening Rodl's theorem (2021) (4)
Solution of two fractional packing problems of lovász (2006) (4)
Pure pairs. V. Excluding some long subdivision (2021) (4)
Polynomial bounds for chromatic number VI. Adding a four-vertex path (2022) (4)
Cut Coloring and Circuit Covering (2006) (4)
Excluding the fork and antifork (2020) (4)
Pure pairs. IV. Trees in bipartite graphs (2020) (4)
Subdivided Claws and the Clique-Stable Set Separation Property (2019) (3)
Counting paths in digraphs (2010) (3)
Bad news for chordal partitions (2017) (3)
Solution of three problems of Cornuéjols (2008) (3)
Three steps towards Gyárfás ’ conjecture (2014) (3)
Even pairs and prism corners in square-free Berge graphs (2018) (3)
Polynomial bounds for chromatic number. V. Excluding a tree of radius two and a complete multipartite graph (2022) (3)
Dense minors of graphs with independence number two (2022) (3)
Girth Six Cubic Graphs Have Petersen Minors (2014) (3)
Pure pairs. II. Sparse graphs without linear anticomplete pairs (2020) (2)
Corrigendum to "Even pairs and prism corners in square-free Berge graphs" [J. Combin. Theory, Ser. B 131 (2018) 12-39] (2018) (2)
Holes with hats and Erdős-Hajnal (2020) (2)
A note on simplicial cliques (2020) (2)
Induced Subgraphs of Graphs with Large Chromatic Number. III. Long Holes (2016) (2)
Some Structural Properties of Unitary Addition Cayley Graphs (2020) (2)
Small families under subdivision. (2019) (2)
Corrigendum to "Bisimplicial vertices in even-hole-free graphs" (2020) (2)
Consecutive holes (2015) (2)
Graph structure theory : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors, held June 22 to July 5, 1991, with support from the National Science Foundation and the Office of Naval Research (1993) (2)
Graphs with all holes the same length (2021) (2)
Cops and robbers on P5-free graphs (2023) (2)
Excluding a Substar and an Antisubstar (2015) (2)
Finding minimum clique capacity (2012) (2)
Claw-free graphs I . Clique cutsets (1)
Short Directed Cycles in Bipartite Digraphs (2018) (1)
Discharging cartwheels (2014) (1)
Cycle-touching graphs (2022) (1)
Induced paths in sparse cycle-touching graphs (2022) (1)
Polynomial bounds for chromatic number VII. Disjoint holes (2022) (1)
Finding balanced skew partitions in perfect graphs (2015) (1)
Near-domination in graphs (2017) (1)
Proof of a conjecture of Bowlin and Brin on four-colouring triangulations (2014) (1)
A Structure Theorem for Claw-Free Perfect Graphs (1)
Induced subgraphs of graphs with large chromatic number . XII . Two-legged caterpillars (2017) (1)
Induced paths in graphs without anticomplete cycles (2022) (1)
Reconizing graphic matroids (1981) (1)
Simplicial cliques in claw-free graphs (2012) (1)
Graph Structure Theory: Proceedings of a Joint Summer Research Conference on Graph Minors Held June 22 to July 5, 1991, at the University of Washington, Seattle. Contemporary Mathematics 147 (1991) (1)
Pure pairs. X. Excluding six-vertex tournaments (2021) (1)
Reducibility in the Four-Color Theorem (2014) (1)
New examples of minimal non-strongly-perfect graphs (2020) (0)
A counterexample to a conjecture of Schwartz (2012) (0)
Linear representation of matroids (1986) (0)
Finding minimum clique capacity (2012) (0)
A pr 2 01 9 Detecting a long odd hole (2019) (0)
Holes with hats and Erd\H{o}s-Hajnal (2020) (0)
Pure pairs. IX. Bonsai trees (2021) (0)
Note Note on the Production of (2003) (0)
THE 4-COLOR PROBLEM (2008) (0)
Perfect matchings in planar cubic graphs (2012) (0)
C O ] 1 D ec 2 01 3 BIPARTITE MINORS (0)
C O ] 1 9 O ct 2 02 1 Graphs with all holes the same length (2021) (0)
Counterexample to a conjecture of Jeurissen (1978) (0)
Packing seagulls (2012) (0)
Colouring graphs with no odd holes, and other stories (2015) (0)
C O ] 2 O ct 2 01 5 Excluding A Grid Minor In Planar Digraphs (0)
Pure pairs. X. Tournaments and the strong Erdos-Hajnal property (2022) (0)
Polynomial bounds for chromatic number VIII. Excluding a path and a complete multipartite graph (2023) (0)
Bipartite graphs with no $K_6$ minor (2022) (0)
ON FORBIDDEN MINORS FOR GP ( 3 ) (2010) (0)
On Packing T-Joins (2007) (0)
Variants of Woodall's conjecture (2013) (0)
5-minute presentations by L. Postle, B. Reed, J. Rus, G. Salazar, A. Scott, P. Seymour, J. Širáň, G. Tóth, P. Whalen, D. Wood, H. Wu, M. Yancey, L. Yepremyan, L. Yuditsky, Y. Zhao (2013) (0)
2 5 M ar 2 01 7 CYCLICALLY FIVE – CONNECTED CUBIC GRAPHS (2021) (0)
Clique covers of H-free graphs (2022) (0)
C O ] 6 M ay 2 02 0 Holes with hats and (2020) (0)
Induced subgraphs of graphs with large chromatic number. XIV. Excluding a biclique and an induced tree (2021) (0)
A letter from the editors (2005) (0)
Even Pairs and Prism Corners in Berge Graphs (2016) (0)
Polyhedral combinatorics : proceedings of a DIMACS workshop : June 12-16, 1989 (1990) (0)
Proof of the Kalai-Meshulam conjecture (2020) (0)
A note on the Gy\'arf\'as-Sumner conjecture (2023) (0)
Excluding a near-clique and a near-anticlique (2012) (0)
Induced Subgraphs and Subtournaments (2012) (0)
Extending the GyárfásSumner conjecture (2014) (0)
Pure pairs. IX. Transversal trees (2021) (0)
Concatenating Bipartite Graphs (2019) (0)
5-minute presentations by D. Archdeacon, E. Berger, B. Bokal, S. Cabello, R. Churchley, V. Dujmović, Z. Dvorak, K. Edwards, M. Ellingham, J. Fox, R. Fulek, G. Gauthier (2013) (0)
Caterpillars in Erd\H{o}s-Hajnal (2018) (0)
Short Directed Cycles in Bipartite Digraphs (2020) (0)
On a problem of El-Zahar and Erdoos (2023) (0)
5-minute presentations by L. Goddyn, P. Haxell, R. Kim, T. Klimosova, A. Kostochka, Z. Li, C. Liu, B. Mohar, J. Noel, S. Norin, J. Pach, M. Plumettaz, L. Postle (2013) (0)
Excluding paths and antipaths (2014) (0)
Detecting a Long Odd Hole (2020) (0)
1 Hadwiger ’ s conjecture and seagulls (2016) (0)
Tournaments and colouring Citation (2012) (0)
Pure Pairs. II. Excluding All Subdivisions of A Graph (2021) (0)
The Minimal Automorphism-Free Tree (2013) (0)

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