Acyclic Coloring of Graphs of Maximum Degree ∆

@inproceedings{Fertin2005AcyclicCO,
  title={Acyclic Coloring of Graphs of Maximum Degree ∆},
  author={Guillaume Fertin and Andr{\'e} Raspaud},
  year={2005}
}
An acyclic coloring of a graph G is a coloring of its vertices such that: (i) no two neighbors in G are assigned the same color and (ii) no bicolored cycle can exist in G. The acyclic chromatic number of G is the least number of colors necessary to acyclically color G, and is denoted by a(G). We show that any graph of maximum degree ∆ has acyclic chromatic number at most ∆(∆−1) 2 for any ∆ ≥ 5, and we give an O(n∆) algorithm to acyclically color any graph of maximum degree ∆ with the above… CONTINUE READING