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Some remarks about factors of graphs

✍ Scribed by José R. Correa; Martín Matamala

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
148 KB
Volume
57
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A (g, f)‐factor of a graph is a subset F of E such that for all $v \in V$, $g(v)\le {\rm deg}_{F}(v)\le f(v)$. Lovasz gave a necessary and sufficient condition for the existence of a (g, f)‐factor. We extend, to the case of edge‐weighted graphs, a result of Kano and Saito who showed that if $g(v)< \lambda {\rm deg}_{E}(v) < f (v)$ for any $\lambda\in [0,1]$, then a (g, f)‐factor always exist. In addition, we use results of Anstee to provide new necessary and sufficient conditions for the existence of a (g, f)‐factor. © 2008 Wiley Periodicals, Inc. J Graph Theory 57: 265–274, 2008

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