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Two-factors each component of which contains a specified vertex

✍ Scribed by Yoshimi Egawa; Hikoe Enomoto; Ralph J. Faudree; Hao Li; Ingo Schiermeyer

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 115 KB
Volume: 43
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10113

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✦ Synopsis

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~i~ ∈ V(C~i~) for (1 ≤ i ≤ k) if $n = 3K,\delta(G)\ge,{{7k-2}\over {3}}$ or 3__k__ + 1 ≤ n ≤ 4__k__, $\delta (G),\ge,{{2n+k-3}\over {3}}$ or 4__k__ ≤ n ≤ 6__k__ − 3,δ(G) ≥ 3__k__ − 1 or n ≥ 6__k__ − 3, $\delta(G)\ge {{n}\over {2}}$. Examples are described that indicate this result is sharp. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 188–198, 2003

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