On the 1-factors of n-connected graphs

Joseph Zaks

doi:10.1016/0095-8956(71)90027-X

On the 1-factors of n-connected graphs

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

Abstract

L. W. Beineke and M. D. Plummer have recently proved [1] that every n-connected graph with a 1-factor has at least n different 1-factors. The main purpose of this paper is to prove that every n-connected graph with a 1-factor has at least as many as n(n - 2)(n - 4) ... 4 · 2, (or: n(n - 2)(n - 4) ... 5 · 3) 1-factors. The main lemma used is: if a 2-connected graph G has a 1-factor, then G contains a vertex V (and even two such vertices), such that each edge of G, incident to V, belongs to some 1-factor of G.

Original language	English
Pages (from-to)	169-180
Number of pages	12
Journal	Journal of Combinatorial Theory. Series B
Volume	11
Issue number	2
DOIs	https://doi.org/10.1016/0095-8956(71)90027-X
State	Published - Oct 1971
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0095-8956(71)90027-X

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abstract = "L. W. Beineke and M. D. Plummer have recently proved [1] that every n-connected graph with a 1-factor has at least n different 1-factors. The main purpose of this paper is to prove that every n-connected graph with a 1-factor has at least as many as n(n - 2)(n - 4) ... 4 · 2, (or: n(n - 2)(n - 4) ... 5 · 3) 1-factors. The main lemma used is: if a 2-connected graph G has a 1-factor, then G contains a vertex V (and even two such vertices), such that each edge of G, incident to V, belongs to some 1-factor of G.",

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AB - L. W. Beineke and M. D. Plummer have recently proved [1] that every n-connected graph with a 1-factor has at least n different 1-factors. The main purpose of this paper is to prove that every n-connected graph with a 1-factor has at least as many as n(n - 2)(n - 4) ... 4 · 2, (or: n(n - 2)(n - 4) ... 5 · 3) 1-factors. The main lemma used is: if a 2-connected graph G has a 1-factor, then G contains a vertex V (and even two such vertices), such that each edge of G, incident to V, belongs to some 1-factor of G.

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On the 1-factors of n-connected graphs

Abstract

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