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k-Factors and Neighbourhoods of Independent Sets in Graphs

✍ Scribed by Woodall, D. R.

Book ID
120094718
Publisher
Oxford University Press
Year
1990
Tongue
English
Weight
159 KB
Volume
s2-41
Category
Article
ISSN
0024-6107

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πŸ“œ SIMILAR VOLUMES

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It is proved that a graph of order n contains a triangle if |N(X )| > 1 3 (n+|X |) for every independent set X of vertices. This bound is sharp.

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## Abstract In 1968, Vizing made the following two conjectures for graphs which are critical with respect to the chromatic index: (1) every critical graph has a 2‐factor, and (2) every independent vertex set in a critical graph contains at most half of the vertices. We prove both conjectures for cr