Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
429036 | Information Processing Letters | 2011 | 6 Pages |
Abstract
An acyclic k-coloring of a graph G is a proper vertex coloring of G, which uses at most k colors, such that the graph induced by the union of every two color classes is a forest. In this note, we prove that every graph with maximum degree six is acyclically 11-colorable, thus improving the main result of Yadav et al. (2009) [11].
► In this paper we need to prove the existence of a certain kind of spanning trees in regular graphs. ► A good spanning tree of a Δ regular graph G is a spanning tree T such that T contains a vertex adjacent to Δ−1Δ−1 leaves. ► We then use such good spanning trees to prove our main result on acyclic colorings. ► Every graph with maximum degree 6 is acyclically 11-colorable.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Hervé Hocquard,