Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  451.05040
Autor:  Erdös, Paul; Harary, Frank; Klawe, Maria
Title:  Residually-complete graphs. (In English)
Source:  Ann. Discrete Math. 6, 117-123 (1980).
Review:  If G is a graph such that the deletion from G of the points in saech closed neighborhood results in the complete graph Kn, then we say that G is Kn-residual. Simularly, if the removal of m consecutive closed neighborhoods yields Kn, then G is called m-Kn-residual. We determine the minimum order of the m-Kn-residual graphs for all m and n. It is further shown that for n \geq 2, Kn+1× K2 is a connection K2-residual graph of minimum order and that, for n \geq 5, it is the only such graph. For n = 3 and n = 4 there i one other such graph and for n = 2, C5 is the only such graph.
Reviewer:  R.L.Hemminger
Classif.:  * 05C99 Graph theory
                   05C35 Extremal problems (graph theory)
Keywords:  complete graphs; residual graphs

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