Several sufficient conditions of a normal graph in conditional coloring
MA Ying-xue · Journal of Shandong University · 2011
For positive integer r,a r-conditional coloring of a graph G is a proper vertex coloring of G such that every vertex v of degree d(v) in G is adjacent to vertices with at least min{r,d(v)} different colors.A graph G is r-normal,if the r-conditional chromatic number of G equals the chromatic number of G.The conditions,which are sufficient for a graph to be normal,are given.Some examples are given to illustrate the conditions are not necessary.