J4 ›› 2011, Vol. 46 ›› Issue (2): 42-44.
• Articles •
SUN Lei, MA Ying-xue
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.
conditional coloring; conditional chromatic number; normal graph
SUN Lei, MA Ying-xue. Several sufficient conditions of a normal graph in conditional coloring[J].J4, 2011, 46(2): 42-44.
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