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## Vertigan, Dirk

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 Author ID: vertigan.dirk Published as: Vertigan, D.; Vertigan, D. L.; Vertigan, Dirk External Links: MGP
 Documents Indexed: 31 Publications since 1990
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#### Co-Authors

 5 single-authored 10 Oxley, James G. 8 Ding, Guoli 8 Oporowski, Bogdan 8 Whittle, Geoffrey P. 3 Geelen, James F. 3 Sanders, Daniel P. 3 Welsh, Dominic J. A. 2 Colbourn, Charles J. 2 DeVos, Matthew 2 Provan, J. Scott 2 Semple, Charles 1 Alon, Noga M. 1 Cazaran, Jilyana 1 Chun, Carolyn 1 Colin de Verdière, Yves 1 Geelen, Jim 1 Gitler, Isidoro 1 Goddyn, Luis A. 1 Jaeger, François 1 Kelarev, Andrei Vladimirovich 1 Massey, David Bradley 1 Mohar, Bojan 1 Quinn, Stephen J. 1 Reed, Bruce Alan 1 Seymour, Paul D. 1 Simion, Rodica E. 1 Stanley, Richard Peter 1 Thomas, Robin 1 Zhu, Xuding 1 Ziegler, Günter Matthias
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#### Serials

 14 Journal of Combinatorial Theory. Series B 2 Transactions of the American Mathematical Society 2 Combinatorica 2 Combinatorics, Probability and Computing 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Commentarii Mathematici Helvetici 1 Journal of Graph Theory 1 Semigroup Forum 1 SIAM Journal on Computing 1 Advances in Applied Mathematics 1 Graphs and Combinatorics 1 Annals of Combinatorics
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#### Fields

 29 Combinatorics (05-XX) 5 Computer science (68-XX) 2 Associative rings and algebras (16-XX) 2 Information and communication theory, circuits (94-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistical mechanics, structure of matter (82-XX)

#### Citations contained in zbMATH Open

29 Publications have been cited 490 times in 386 Documents Cited by Year
On the computational complexity of the Jones and Tutte polynomials. Zbl 0747.57006
Jaeger, François; Vertigan, D. L.; Welsh, D. J. A.
1990
On inequivalent representations of matroids over finite fields. Zbl 0856.05021
Oxley, James; Vertigan, Dirk
1996
Excluding any graph as a minor allows a low tree-width 2-coloring. Zbl 1042.05036
DeVos, Matt; Ding, Guoli; Oporowski, Bogdan; Sanders, Daniel P.; Reed, Bruce; Seymour, Paul; Vertigan, Dirk
2004
Partitioning into graphs with only small components. Zbl 1023.05045
Alon, Noga; Ding, Guoli; Oporowski, Bogdan; Vertigan, Dirk
2003
Planar electric networks. II. Zbl 0853.05074
Colin de Verdière, Yves; Gitler, Isidoro; Vertigan, Dirk
1996
The computational complexity of Tutte invariants for planar graphs. Zbl 1089.05017
Vertigan, Dirk
2006
Generalized $$\Delta\text{--}Y$$ exchange and $$k$$-regular matroids. Zbl 1024.05017
Oxley, James; Semple, Charles; Vertigan, Dirk
2000
An algorithm for computing the minimum distances of extensions of BCH codes embedded in semigroup rings. Zbl 1145.94023
Cazaran, J.; Kelarev, A. V.; Quinn, S. J.; Vertigan, D.
2006
Totally free expansions of matroids. Zbl 1048.05020
Geelen, James; Oxley, James; Vertigan, Dirk; Whittle, Geoff
2002
The computational complexity of the Tutte plane: The bipartite case. Zbl 0793.05091
Vertigan, D. L.; Welsh, D. J. A.
1992
Surfaces, tree-width, clique-minors, and partitions. Zbl 1029.05041
Ding, Guoli; Oporowski, Bogdan; Sanders, Daniel P.; Vertigan, Dirk
2000
Unavoidable minors of large 3-connected binary matroids. Zbl 0856.05022
Ding, Guoli; Oporowski, Bogdan; Oxley, James; Vertigan, Dirk
1996
Weak maps and stabilizers of classes of matroids. Zbl 0919.05010
Geelen, James; Oxley, James; Vertigan, Dirk; Whittle, Geoff
1998
Partitioning graphs of bounded tree-width. Zbl 0924.05022
Ding, Guoli; Oporowski, Bogdan; Sanders, Daniel P.; Vertigan, Dirk
1998
Unavoidable minors of large 3-connected matroids. Zbl 0897.05020
Ding, Guoli; Oporowski, Bogdan; Oxley, James; Vertigan, Dirk
1997
Coloring-flow duality of embedded graphs. Zbl 1065.05034
DeVos, Matt; Goddyn, Luis; Mohar, Bojan; Vertigan, Dirk; Zhu, Xuding
2005
Bicycle dimension and special points of the Tutte polynomial. Zbl 1023.05030
Vertigan, Dirk
1998
Large non-planar graphs and an application to crossing-critical graphs. Zbl 1223.05153
Ding, Guoli; Oporowski, Bogdan; Thomas, Robin; Vertigan, Dirk
2011
A new approach to solving three combinatorial enumeration problems on planar graphs. Zbl 0833.05043
Colbourn, Charles J.; Provan, J. Scott; Vertigan, Dirk
1995
On maximum-sized near-regular and $$\root 6\of{1}$$-matroids. Zbl 0915.05034
Oxley, James; Vertigan, Dirk; Whittle, Geoff
1998
The complexity of computing the Tutte polynomial on transversal matroids. Zbl 0821.05011
Colbourn, Charles J.; Provan, J. Scott; Vertigan, Dirk
1995
Dowling geometries representable over rings. Zbl 1310.05054
Vertigan, Dirk
2015
Unavoidable parallel minors of 4-connected graphs. Zbl 1215.05170
Chun, Carolyn; Ding, Guoli; Oporowski, Bogdan; Vertigan, Dirk
2009
Latroids and their representation by codes over modules. Zbl 1043.05029
Vertigan, Dirk
2004
A short proof of non-GF(5)-representability of matroids. Zbl 1050.05024
Geelen, Jim; Oxley, James; Vertigan, Dirk; Whittle, Geoff
2004
Lê numbers of arrangements and matroid identities. Zbl 0884.05029
Massey, David B.; Simion, Rodica; Stanley, Richard P.; Vertigan, Dirk; Welsh, Dominic J. A.; Ziegler, Günter M.
1997
On the excluded minors for quaternary matroids. Zbl 1023.05028
Geelen, J. F.; Oxley, J. G.; Vertigan, D. L.; Whittle, G. P.
2000
A 2-isomorphism theorem for hypergraphs. Zbl 0888.05045
Vertigan, Dirk; Whittle, Geoff
1997
Recognizing polymatroids associated with hypergraphs. Zbl 0793.05045
Vertigan, Dirk; Whittle, Geoff
1993
Dowling geometries representable over rings. Zbl 1310.05054
Vertigan, Dirk
2015
Large non-planar graphs and an application to crossing-critical graphs. Zbl 1223.05153
Ding, Guoli; Oporowski, Bogdan; Thomas, Robin; Vertigan, Dirk
2011
Unavoidable parallel minors of 4-connected graphs. Zbl 1215.05170
Chun, Carolyn; Ding, Guoli; Oporowski, Bogdan; Vertigan, Dirk
2009
The computational complexity of Tutte invariants for planar graphs. Zbl 1089.05017
Vertigan, Dirk
2006
An algorithm for computing the minimum distances of extensions of BCH codes embedded in semigroup rings. Zbl 1145.94023
Cazaran, J.; Kelarev, A. V.; Quinn, S. J.; Vertigan, D.
2006
Coloring-flow duality of embedded graphs. Zbl 1065.05034
DeVos, Matt; Goddyn, Luis; Mohar, Bojan; Vertigan, Dirk; Zhu, Xuding
2005
Excluding any graph as a minor allows a low tree-width 2-coloring. Zbl 1042.05036
DeVos, Matt; Ding, Guoli; Oporowski, Bogdan; Sanders, Daniel P.; Reed, Bruce; Seymour, Paul; Vertigan, Dirk
2004
Latroids and their representation by codes over modules. Zbl 1043.05029
Vertigan, Dirk
2004
A short proof of non-GF(5)-representability of matroids. Zbl 1050.05024
Geelen, Jim; Oxley, James; Vertigan, Dirk; Whittle, Geoff
2004
Partitioning into graphs with only small components. Zbl 1023.05045
Alon, Noga; Ding, Guoli; Oporowski, Bogdan; Vertigan, Dirk
2003
Totally free expansions of matroids. Zbl 1048.05020
Geelen, James; Oxley, James; Vertigan, Dirk; Whittle, Geoff
2002
Generalized $$\Delta\text{--}Y$$ exchange and $$k$$-regular matroids. Zbl 1024.05017
Oxley, James; Semple, Charles; Vertigan, Dirk
2000
Surfaces, tree-width, clique-minors, and partitions. Zbl 1029.05041
Ding, Guoli; Oporowski, Bogdan; Sanders, Daniel P.; Vertigan, Dirk
2000
On the excluded minors for quaternary matroids. Zbl 1023.05028
Geelen, J. F.; Oxley, J. G.; Vertigan, D. L.; Whittle, G. P.
2000
Weak maps and stabilizers of classes of matroids. Zbl 0919.05010
Geelen, James; Oxley, James; Vertigan, Dirk; Whittle, Geoff
1998
Partitioning graphs of bounded tree-width. Zbl 0924.05022
Ding, Guoli; Oporowski, Bogdan; Sanders, Daniel P.; Vertigan, Dirk
1998
Bicycle dimension and special points of the Tutte polynomial. Zbl 1023.05030
Vertigan, Dirk
1998
On maximum-sized near-regular and $$\root 6\of{1}$$-matroids. Zbl 0915.05034
Oxley, James; Vertigan, Dirk; Whittle, Geoff
1998
Unavoidable minors of large 3-connected matroids. Zbl 0897.05020
Ding, Guoli; Oporowski, Bogdan; Oxley, James; Vertigan, Dirk
1997
Lê numbers of arrangements and matroid identities. Zbl 0884.05029
Massey, David B.; Simion, Rodica; Stanley, Richard P.; Vertigan, Dirk; Welsh, Dominic J. A.; Ziegler, Günter M.
1997
A 2-isomorphism theorem for hypergraphs. Zbl 0888.05045
Vertigan, Dirk; Whittle, Geoff
1997
On inequivalent representations of matroids over finite fields. Zbl 0856.05021
Oxley, James; Vertigan, Dirk
1996
Planar electric networks. II. Zbl 0853.05074
Colin de Verdière, Yves; Gitler, Isidoro; Vertigan, Dirk
1996
Unavoidable minors of large 3-connected binary matroids. Zbl 0856.05022
Ding, Guoli; Oporowski, Bogdan; Oxley, James; Vertigan, Dirk
1996
A new approach to solving three combinatorial enumeration problems on planar graphs. Zbl 0833.05043
Colbourn, Charles J.; Provan, J. Scott; Vertigan, Dirk
1995
The complexity of computing the Tutte polynomial on transversal matroids. Zbl 0821.05011
Colbourn, Charles J.; Provan, J. Scott; Vertigan, Dirk
1995
Recognizing polymatroids associated with hypergraphs. Zbl 0793.05045
Vertigan, Dirk; Whittle, Geoff
1993
The computational complexity of the Tutte plane: The bipartite case. Zbl 0793.05091
Vertigan, D. L.; Welsh, D. J. A.
1992
On the computational complexity of the Jones and Tutte polynomials. Zbl 0747.57006
Jaeger, François; Vertigan, D. L.; Welsh, D. J. A.
1990
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#### Cited by 512 Authors

 24 Whittle, Geoffrey P. 19 Oxley, James G. 13 Vertigan, Dirk 12 Welsh, Dominic J. A. 9 Colbourn, Charles J. 9 Nešetřil, Jaroslav 9 Ossona de Mendez, Patrice 8 Ding, Guoli 8 Geelen, Jim 8 Kelarev, Andrei Vladimirovich 8 Mayhew, Dillon 7 Makowsky, Johann-Andreas 7 Semple, Charles 7 Shah, Tariq 7 Yearwood, John L. 6 de Andrade, Antonio Aparecido 6 Diao, Yuanan 6 Goldberg, Leslie Ann 6 Oporowski, Bogdan 6 Ueckerdt, Torsten 6 van Zwam, Stefan H. M. 5 Hall, Rhiannon 5 Hetyei, Gábor 5 Jerrum, Mark R. 5 Mohar, Bojan 5 Oum, Sang-Il 5 Robbins, Jakayla R. 5 Wood, David Ronald 5 Zhu, Xuding 4 Brown, Jason Ira 4 Farr, Graham E. 4 Geelen, James F. 4 Gitler, Isidoro 4 Guo, Heng 4 Jin, Xian’an 4 Liotta, Giuseppe 4 Moffatt, Iain 4 Montecchiani, Fabrizio 4 Reid, Talmage James 4 Watters, Paul A. 4 Zhou, Xiangqian 3 Axenovich, Maria A. 3 Ben-Efraim, Aner 3 Brettell, Nick 3 Chun, Deborah 3 Clark, Ben 3 Colin de Verdière, Yves 3 Dell, Holger 3 Dvořák, Zdeněk 3 Ellis-Monaghan, Joanna A. 3 Gerards, Bert 3 Gordon, Gary 3 Guevara Vasquez, Fernando 3 Hinson, Kenneth 3 Kawarabayashi, Ken-ichi 3 Kenyon, Richard W. 3 Knauer, Kolja B. 3 Kwon, Ojoung 3 Las Vergnas, Michel 3 Marzuoli, Annalisa 3 Matoušek, Jiří 3 Merino, Criel 3 Pendavingh, Rudi A. 3 Provan, J. Scott 3 Rasetti, Mario 3 Seymour, Paul D. 3 Slilaty, Daniel C. 3 Szabó, Tibor 3 Tardos, Gábor 2 Abawajy, Jemal H. 2 Aharonov, Dorit 2 Alon, Noga M. 2 Andrzejak, Artur 2 Annan, James D. 2 Berke, Robert 2 Bläser, Markus 2 Bonin, Joseph E. 2 Bordewich, Magnus 2 Borowiecki, Mieczysław 2 Brand, Cornelius 2 Brijder, Robert 2 Chen, Rong 2 Chun, Carolyn 2 Curticapean, Radu 2 Dasbach, Oliver T. 2 de Mier, Anna 2 Di Giacomo, Emilio 2 Didimo, Walter 2 Dziobiak, Stan 2 Esperet, Louis 2 Freedman, Michael Hartley 2 Galashin, Pavel 2 Gimbel, John G. 2 Golovach, Petr A. 2 Gonçalves, Daniel 2 Goodall, Andrew J. 2 Grace, Kevin 2 Haxell, Penny E. 2 Heldt, Daniel 2 Hong, Yuan ...and 412 more Authors
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#### Cited in 110 Serials

 42 Journal of Combinatorial Theory. Series B 38 Discrete Mathematics 27 European Journal of Combinatorics 20 Advances in Applied Mathematics 17 Combinatorics, Probability and Computing 13 Theoretical Computer Science 13 SIAM Journal on Discrete Mathematics 11 Discrete Applied Mathematics 10 Journal of Graph Theory 10 Journal of Knot Theory and its Ramifications 7 Annals of Combinatorics 5 Combinatorica 5 Graphs and Combinatorics 4 Semigroup Forum 4 Information and Computation 4 Computational Complexity 4 The Electronic Journal of Combinatorics 3 Advances in Mathematics 3 Annales de l’Institut Fourier 3 Journal of Combinatorial Theory. Series A 3 Algorithmica 3 Discrete & Computational Geometry 3 Annals of Operations Research 3 Random Structures & Algorithms 3 Linear Algebra and its Applications 3 Journal of Mathematical Chemistry 2 Communications in Algebra 2 Journal of Statistical Physics 2 Duke Mathematical Journal 2 Designs, Codes and Cryptography 2 Journal of Algebraic Combinatorics 2 Computational and Applied Mathematics 2 Theory of Computing Systems 2 Geometry & Topology 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Journal of Algebra and its Applications 2 International Journal of Geometric Methods in Modern Physics 2 Journal of Physics A: Mathematical and Theoretical 2 Asian-European Journal of Mathematics 2 Discrete Mathematics, Algorithms and Applications 1 Artificial Intelligence 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Information Processing Letters 1 Israel Journal of Mathematics 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Linear and Multilinear Algebra 1 Physica A 1 Reviews of Modern Physics 1 Acta Mathematica 1 Anais da Academia Brasileira de Ciências 1 Applied Mathematics and Computation 1 Ars Combinatoria 1 Inventiones Mathematicae 1 Journal of Computer and System Sciences 1 Journal für die Reine und Angewandte Mathematik 1 Kybernetika 1 Memoirs of the American Mathematical Society 1 Networks 1 SIAM Journal on Computing 1 Transactions of the American Mathematical Society 1 Topology and its Applications 1 Applied Mathematics Letters 1 Journal of the American Mathematical Society 1 Economics Letters 1 Computational Geometry 1 International Journal of Algebra and Computation 1 International Journal of Foundations of Computer Science 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Games and Economic Behavior 1 International Journal of Computer Mathematics 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Journal on Applied Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Experimental Mathematics 1 Journal of Combinatorial Designs 1 Discussiones Mathematicae. Graph Theory 1 Journal of Difference Equations and Applications 1 ELA. The Electronic Journal of Linear Algebra 1 Séminaire Lotharingien de Combinatoire 1 Open Systems & Information Dynamics 1 Journal of Graph Algorithms and Applications 1 New Journal of Physics 1 Annals of Mathematics. Second Series 1 LMS Journal of Computation and Mathematics 1 Communications in Contemporary Mathematics 1 Annales Henri Poincaré 1 Journal of the Australian Mathematical Society 1 Portugaliae Mathematica. Nova Série 1 Quantum Information Processing 1 Journal of Discrete Algorithms 1 International Journal of Quantum Information 1 Journal of Statistical Mechanics: Theory and Experiment 1 Discrete Optimization 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Mathematics in Computer Science 1 Networks and Heterogeneous Media ...and 10 more Serials
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#### Cited in 38 Fields

 292 Combinatorics (05-XX) 88 Computer science (68-XX) 48 Manifolds and cell complexes (57-XX) 26 Information and communication theory, circuits (94-XX) 23 Statistical mechanics, structure of matter (82-XX) 17 Quantum theory (81-XX) 16 Convex and discrete geometry (52-XX) 11 Probability theory and stochastic processes (60-XX) 9 Group theory and generalizations (20-XX) 9 Operations research, mathematical programming (90-XX) 8 Number theory (11-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 6 Associative rings and algebras (16-XX) 6 Partial differential equations (35-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Biology and other natural sciences (92-XX) 4 Commutative algebra (13-XX) 4 Category theory; homological algebra (18-XX) 3 Mathematical logic and foundations (03-XX) 3 Algebraic geometry (14-XX) 3 Potential theory (31-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Field theory and polynomials (12-XX) 2 Numerical analysis (65-XX) 1 History and biography (01-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX)