## 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
On the Size of Edge Chromatic Critical Graphs
β Scribed by Daniel P. Sanders; Yue Zhao
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 85 KB
- Volume
- 86
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, by applying the discharging method, we prove that if
π SIMILAR VOLUMES
## 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
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.
## Abstract A graph __G__ with maximum degree Ξ and edge chromatic number $\chi\prime({G}) > \Delta$ is __edge__βΞβ__critical__ if $\chi\prime{(G-e)} = \Delta$ for every edge __e__ of __G__. It is proved that the average degree of an edgeβΞβcritical graph is at least ${2\over 3}{(\Delta+1)}$ if $\D
## 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 2βfactor, and (2) every independent vertex set in a critical graph contains at most half of the vertices. We prove both conjectures for cr