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Cliques and niche graphs. (English) Zbl 0862.05066

The study of niche graphs was begun in 1986. A paper detailing initial results was published in 1989, see C. Cable, K. F. Jones, J. R. Lundgren, and S. Seager [Discrete Appl. Math. 23, No. 3, 231-241 (1989; Zbl 0677.05039)]. A subsequent paper on niche graphs is [S. Bowser and C. A. Cable, Discrete Appl. Math. 30, No. 2/3, 101-108 (1991; Zbl 0713.05032)]. In this paper we discuss results concerning the relationship between maximal clique structure of a graph and its niche number as well as a result describing a class of trees with niche number zero.

MSC:

05C35 Extremal problems in graph theory
05C20 Directed graphs (digraphs), tournaments
05C05 Trees
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