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Vertex-disjoint cycles containing specified vertices in a bipartite graph

✍ Scribed by Guantao Chen; Hikoe Enomoto; Ken-ichi Kawarabayashi; Katsuhiro Ota; Dingjun Lou; Akira Saito

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 184 KB
Volume: 46
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10159

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✦ Synopsis

Abstract

A minimum degree condition is given for a bipartite graph to contain a 2‐factor each component of which contains a previously specified vertex. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 145–166, 2004

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## Abstract We obtain a sharp minimum degree condition δ (G) ≥ $\lfloor {\sqrt {\phantom{n^2}n+k^2-3k+1}}\rfloor + 2k-1$ of a graph __G__ of order __n__ ≥ 3__k__ guaranteeing that, for any __k__ distinct vertices, __G__ contains __k__ vertex‐disjoint cycles of length at most four each of which cont