Elsevier

Discrete Mathematics

Volume 309, Issue 16, 28 August 2009, Pages 5242-5247
Discrete Mathematics

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Edge-deletable IM-extendable graphs with minimum number of edges

https://doi.org/10.1016/j.disc.2009.03.048Get rights and content
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Abstract

A graph G is induced matching extendable, shortly IM-extendable, if every induced matching of G is included in a perfect matching of G. For a nonnegative integer k, a graph G is called a k-edge-deletable IM-extendable graph, if, for every FE(G) with |F|=k, GF is IM-extendable. In this paper, we characterize the k-edge-deletable IM-extendable graphs with minimum number of edges. We show that, for a positive integer k, if G is ak-edge-deletable IM-extendable graph on 2n vertices, then |E(G)|(k+2)n; furthermore, the equality holds if and only if either GKk+2,k+2, or k=4r2 for some integer r3 and GC5[N2r], where N2r is the empty graph on 2r vertices and C5[N2r] is the graph obtained from C5 by replacing each vertex with a graph isomorphic to N2r.

Keywords

Induced matching
IM-extendable
k-edge-deletable IM-extendable graphs

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Project partially supported by NFSC-RGC (70731160633), NSFC (10671183) and SRFDP (20070459002).