In this paper, we prove that any edge-coloring critical graph G with maximum degree ΒΏ (11 + β 49 -24 )=2, where 6 1, has the size at least 3(|V (G)| -) + 1 if 6 7 or if ΒΏ 8 and |V (G)| ΒΏ 2 --4 -( + 6)=( -6), where is the minimum degree of G. It generalizes a result of Sanders and Zhao.
Edge-coloring critical graphs with high degree
β Scribed by Lian-ying Miao; Jian-liang Wu
- Book ID
- 108315771
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 72 KB
- Volume
- 257
- Category
- Article
- ISSN
- 0012-365X
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## Abstract An __acyclic__ edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The __acyclic chromatic index__ of a graph is the minimum number __k__ such that there is an acyclic edge coloring using __k__ colors and is denoted by __a__β²(__G__). It was conj
An edge-face coloring of a plane graph with edge set E and face set F is a coloring of the elements of E βͺF so that adjacent or incident elements receive different colors. Borodin [Discrete Math 128(1-3): [21][22][23][24][25][26][27][28][29][30][31][32][33] 1994] proved that every plane graph of max