In this paper, by applying the discharging method, we prove that if
New lower bounds for the size of edge chromatic critical graphs
β Scribed by Yue Zhao
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 108 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0364-9024
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β¦ Synopsis
Abstract
In this paper, by applying the discharging method, we obtain new lower bounds for the size of edge chromatic critical graphs for small maximum degree Ξ. Β© 2004 Wiley Periodicals, Inc. J Graph Theory 46: 81β92, 2004
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In 1968, Vizing conjectured that if G is a -critical graph with n vertices, then (G) β€ n / 2, where (G) is the independence number of G. In this paper, we apply Vizing and Vizing-like adjacency lemmas to this problem and prove that (G)<(((5 -6)n) / (8 -6))<5n / 8 if β₯ 6. α§ 2010 Wiley
## Abstract In 1968, Vizing [Uaspekhi Mat Nauk 23 (1968) 117β134; Russian Math Surveys 23 (1968), 125β142] conjectured that for any edge chromatic critical graph ${{G}} = ({{V}}, {{E}})$ with maximum degree $\Delta$, $|{{E}}| \geq {{{1}}\over {{2}}}\{(\Delta {{- 1}})|{{V}}| + {{3}}\}$. This conject
## Abstract In this article we first give an upper bound for the chromatic number of a graph in terms of its degrees. This bound generalizes and modifies the bound given in 11. Next, we obtain an upper bound of the order of magnitude ${\cal O}({n}^{{1}-\epsilon})$ for the coloring number of a graph
A graph G with maximum degree and edge chromatic number (G)> is edge--critical if (G -e) = for every edge e of G. It is proved here that the vertex independence number of an edge--critical graph of order n is less than 3 5 n. For large , this improves on the best bound previously known, which was ro
## Abstract We give examples of edgeβchromatic critical graphs __G__ of the following types: (i) of even order and having no 1βfactor, and (ii) of odd order and having a vertex __v__ of minimum degree such that __G__ β __v__ has no 1βfactor. The first disproves a conjecture of S. Fiorini and R. J.