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Vertex-disjoint cycles of length at most four each of which contains a specified vertex

✍ Scribed by Yoshiyas Ishigami

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
157 KB
Volume
37
Category
Article
ISSN
0364-9024

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✦ Synopsis

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 contains one of the k prescribed vertices. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 37–47, 2001

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Two-factors each component of which cont
Two-factors each component of which contains a specified vertex
✍ Yoshimi Egawa; Hikoe Enomoto; Ralph J. Faudree; Hao Li; Ingo Schiermeyer 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 115 KB

## Abstract It is shown that if __G__ is a graph of order __n__ with minimum degree δ(__G__), then for any set of __k__ specified vertices {__v__~1~,__v__~2~,…,__v__~__k__~} ⊂ __V__(__G__), there is a 2‐factor of __G__ with precisely __k__ cycles {__C__~1~,__C__~2~,…,__C__~__k__~} such that __v__~_