On existence of [a,b]-factors avoiding given subgraphs

Details On existence of [a,b]-factors avoiding given subgraphs On existence of [a,b]-factors avoiding given subgraphs

2006-11-03

arxiv.org/abs/math/0611070v1

Mathematics

Combinatorics

13 pages

Scientific paper

For a graph $G = (V(G), E(G))$, let $i(G)$ be the number of isolated vertices in $G$. The {\it isolated toughness} of $G$ is defined as $I(G) = min\{|S|/i(G-S) : S\subseteq V(G), i(G-S)\geq 2\}$ if $G$ is not complete; $I(G)=|V(G)|-1$ otherwise. In this paper, several sufficient conditions in terms of isolated toughness are obtained for the existence of $[a, b]$-factors avoiding given subgraphs, e.g., a set of vertices, a set of edges and a matching, respectively.

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