×

Isolated toughness and existence of \([a,b]\)-factors in graphs. (English) Zbl 1127.05081

Let \(V(G)\) be the vertex set, and let \(i(G)\) be the number of isolated vertices of a graph \(G\). The isolated toughness of \(G\) is defined by
\[ I(G)=\min\{| S| /i(G-S)\,| \,S\subseteq V(G),\, i(G-S)\geq 2\} \]
when \(G\) is not complete and \(I(K_n)=n-1\). The authors present some sufficient conditions for the existence of special factors depending on the isolated toughness. For example, Theorem 1.2 states: Let \(a,b\) be two integers such that \(2\leq a<b\), and let \(G\) be a graph with minimum degree \(\delta\geq a\) such that \(I(G)>a-1+(a-1)/b\). If \(G-S\) has no \((a-1)\)-regular component for any subset \(S\) of \(V(G)\), then \(G\) contains an \([a,b]\)-factor. Theorem 1.2 is an extension of a 1990 result by Katerinis.

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
PDFBibTeX XMLCite