J4 ›› 2012, Vol. 25 ›› Issue (4): 6-9.doi: 10.3976/j.issn.1002-4026.2012.04.002
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LIU Ting, SUN Lei
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Abstract:
Conditional (k,r) coloring of a graph G is a map c:V(G)→{1,2,…,k} for positive integers k and r. It satisfies two conditions that if u,v∈V(G) are adjacent vertices in G, then c(u)≠c(v), and that |c(N(v))|≥ min{|N(v)|,r} for any v∈V(G). The conditional chromatic number of a graph G,χr(G), is the smallest k that makes G have a proper(k,r)coloring. We address the conditional chromatic number of several special types of graphs when r is 3.
Key words: conditional coloring, conditional chromatic number, split graph, Hajós sum
CLC Number:
O157.5
LIU Ting, SUN Lei. Conditional chromatic number of several special types of graphs[J].J4, 2012, 25(4): 6-9.
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