Equitable list point arboricity of graphs
Xin Zhang · Filomat · 2016
A graph G is list point k-arborable if, whenever we are given a k-list assignment L(v) of colors for each vertex v V(G), we can choose a color c(v) L(v) for each vertex v so that each color class induces an acyclic subgraph of G, and is equitable list point k-arborable if G is list point k-arborable and each color appears on at most |V(G)|=k vertices of G. In this paper, we conjecture that every graph G is equitable list point k-arborable for every k ≥ (Δ(G)+1)/2 and settle this for complete graphs, 2-degenerate graphs, 3-degenerate claw-free graphs with maximum degree at least 4, and planar graphs with maximum degree at least 8.