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Factors in graphs with odd-cycle property

✍ Scribed by Ciping Chen; Jianfang Wang

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
634 KB
Volume
112
Category
Article
ISSN
0012-365X

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✦ Synopsis

Chen, C. and J. Wang, Factors in graphs with odd-cycle property, Discrete Mathematics 112 (1993) 29-40.

We present some conditions for the existence of a (g,f)-factor or a (g,f)-parity factor in a graph G with the odd-cycle property that any two odd cycles of G either have a vertex in common or are joined by an edge.

πŸ“œ SIMILAR VOLUMES

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Gyarf&, A., Graphs with k odd cycle lengths, Discrete Mathematics 103 (1992) 41-48. If G is a graph with k z 1 odd cycle lengths then each block of G is either KZk+2 or contains a vertex of degree at most 2k. As a consequence, the chromatic number of G is at most 2k + 2. For a graph G let L(G) deno

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We say that a digraph D has the odd cycle property if there exists an edge subset S such that every cycle of D has an odd number of edges from S. We give necessary and sufficient conditions for a digraph to have the odd cycle property. We also consider the analogous problem for graphs.

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It is shown that any 4-chromatic graph on n vertices contains an odd cycle of length smaller than √ 8n.

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✍ Tao Jiang πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 50 KB

## Abstract It is shown that every 4‐chromatic graph on __n__ vertices contains an odd cycle of length less than $2\sqrt {n}\,+3$. This improves the previous bound given by Nilli [J Graph Theory 3 (1999), 145–147]. Β© 2001 John Wiley & Sons, Inc. J Graph Theory 37: 115–117, 2001