On acyclic colorings of graphs on surfaces
β Scribed by Noga Alon; Bojan Mohar; Daniel P. Sanders
- Book ID
- 112886357
- Publisher
- The Hebrew University Magnes Press
- Year
- 1996
- Tongue
- English
- Weight
- 485 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0021-2172
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π SIMILAR VOLUMES
## Abstract A proper coloring of the edges of a graph __G__ is called __acyclic__ if there is no 2βcolored cycle in __G__. The __acyclic edge chromatic number__ of __G__, denoted by __aβ²__(__G__), is the least number of colors in an acyclic edge coloring of __G__. For certain graphs __G__, __aβ²__(_
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