Bounds for the game coloring number of planar graphs with a specific girth [article]

Keaitsuda Maneeruk Nakprasit, Kittikorn Nakprasit
2016 arXiv   pre-print
Let col_g(G) be the game coloring number of a given graph G. Define the game coloring number of a family of graphs H as col_g(H) := { col_g(G):G ∈H}. Let P_k be the family of planar graphs of girth at least k. We show that col_g(P_7) ≤ 5. This result extends a result about the coloring number by Wang and Zhang WZ11 ( col_g(P_8) ≤ 5). We also show that these bounds are sharp by constructing a graph G where G ∈ col_g(P_k) ≥ 5 for each k ≤ 8 such that col_g(G)=5. As a consequence, col_g(P_k) = 5 for k =7,8.
arXiv:1610.01260v2 fatcat:slimz42zfjexrn7u4xnajtub6i