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

13 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

Access to Document

10.1016/S0195-6698(86)80043-9

Cite this

@article{e0ae5beb86a142948e883325864456d8,

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.",

author = "Seymour, \{P. D.\}",

year = "1986",

doi = "10.1016/S0195-6698(86)80043-9",

language = "English (US)",

volume = "7",

pages = "171--176",

journal = "European Journal of Combinatorics",

issn = "0195-6698",

publisher = "Academic Press",

number = "2",

}

TY - JOUR

T1 - Adjacency in Binary Matroids

AU - Seymour, P. D.

PY - 1986

Y1 - 1986

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/84974018088

UR - https://www.scopus.com/inward/citedby.url?scp=84974018088&partnerID=8YFLogxK

U2 - 10.1016/S0195-6698(86)80043-9

DO - 10.1016/S0195-6698(86)80043-9

M3 - Article

AN - SCOPUS:84974018088

SN - 0195-6698

VL - 7

SP - 171

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

Access to Document

Other files and links

Fingerprint

Cite this