Efficient algorithms for vertex arboricity of planar graphs

Abstract

Acyclic-coloring of a graph G = (V, E) is a partitioning of V, such that the induced subgraph of each partition is acyclic. The minimum number of such partitions of V is defined as the vertex arboricity of G. A linear time algorithm for acyclic-coloring of planar graphs with 3 colors is presented. Next, an O(n2) algorithm is proposed which produces a valid acyclic-2-coloring of a planar graph, if one exists, since there are planar graphs with arboricity 3.