The total chromatic number zt(G) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same colo...
For an integer r > 0, a conditional (k, r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least r in G will be adjacent t...
Hong-Jian Lai, Jianliang Lin, Bruce Montgomery, Ta...
Erdos proved that there are graphs with arbitrarily large girth and chromatic number. We study the extension of this for generalized chromatic numbers. Generalized graph coloring d...