Conflict-free connection number and independence number of a graph [article]

Jing Wang, Meng Ji
2020 arXiv   pre-print
An edge-colored graph G is conflict-free connected if any two of its vertices are connected by a path, which contains a color used on exactly one of its edges. The conflict-free connection number of a connected graph G, denoted by cfc(G), is defined as the minimum number of colors that are required in order to make G conflict-free connected. In this paper, we investigate the relation between the conflict-free connection number and the independence number of a graph. We firstly show that
more » ... (G) for any connected graph G, and an example is given showing that the bound is sharp. With this result, we prove that if T is a tree with Δ(T)≥α(T)+2/2, then cfc(T)=Δ(T).
arXiv:2012.04820v1 fatcat:5fhlh7pfpje5fhlfcj5tvwkghy