A k-forest is a forest in which the maximum degree is k. The k-arboricity denoted Ak(G) is the minimum number of k-forests whose union is the graph G. We show that if G is an m-degenerate graph of maximum degree A, then Ak(G) 5 [(A + (k -1) m -1)/k], k 2 2, and derive several consequences of this in
Acyclic edge coloring of sparse graphs
β Scribed by Yingqian Wang; Ping Sheng
- Book ID
- 118737068
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 285 KB
- Volume
- 312
- 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__). A graph is
An __acyclic edgeβcoloring__ of a graph is a proper edgeβcoloring such that the subgraph induced by the edges of any two colors is acyclic. The __acyclic chromatic index__ of a graph __G__ is the smallest number of colors in an acyclic edgeβcoloring of __G__. We prove that the acyclic chromatic inde