Adjacency in Binary Matroids

P. D. Seymour

doi:10.1016/S0195-6698(86)80043-9

Adjacency in Binary Matroids

P. D. Seymour

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We say that two elements e, f of a binary matroid M are ‘adjacent’ if there is no minor of M isomorphic to ℳ(K₄) which uses both e and f and in which they correspond to opposite edges. We give a good characterization of when two elements are adjacent. In particular, we show that if M is 4-connected, elements e, f are adjacent if and only if M is either graphic or cographic and the elements correspond to adjacent edges of the graph. We deduce a theorem about disjoint paths in graphs.

Original language	English (US)
Pages (from-to)	171-176
Number of pages	6
Journal	European Journal of Combinatorics
Volume	7
Issue number	2
DOIs	https://doi.org/10.1016/S0195-6698(86)80043-9
State	Published - 1986
Externally published	Yes

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1016/S0195-6698(86)80043-9

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title = "Adjacency in Binary Matroids",

abstract = "We say that two elements e, f of a binary matroid M are {\textquoteleft}adjacent{\textquoteright} if there is no minor of M isomorphic to ℳ(K4) which uses both e and f and in which they correspond to opposite edges. We give a good characterization of when two elements are adjacent. In particular, we show that if M is 4-connected, elements e, f are adjacent if and only if M is either graphic or cographic and the elements correspond to adjacent edges of the graph. We deduce a theorem about disjoint paths in graphs.",

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AU - Seymour, P. D.

PY - 1986

Y1 - 1986

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AB - We say that two elements e, f of a binary matroid M are ‘adjacent’ if there is no minor of M isomorphic to ℳ(K4) which uses both e and f and in which they correspond to opposite edges. We give a good characterization of when two elements are adjacent. In particular, we show that if M is 4-connected, elements e, f are adjacent if and only if M is either graphic or cographic and the elements correspond to adjacent edges of the graph. We deduce a theorem about disjoint paths in graphs.

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VL - 7

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EP - 176

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 2

ER -

Adjacency in Binary Matroids

Abstract

All Science Journal Classification (ASJC) codes

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