J4 ›› 2011, Vol. 46 ›› Issue (2): 42-44.

• Articles • Previous Articles     Next Articles

Several sufficient conditions of a normal graph in conditional coloring

SUN Lei, MA Ying-xue   

  1. School of Mathematical Science, Shandong Normal University, Jinan 250014, Shandong, China
  • Received:2009-12-03 Online:2011-02-16 Published:2011-03-30


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.

Key words: conditional coloring; conditional chromatic number; normal graph

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