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Graphs and Combinatorics 7, 1-6 (1991) Combinatorics

Summary: Graphs and Combinatorics 7, 1-6 (1991)
Springer-Verlag 1991
Ramsey GraphsContainManyDistinct
N. Alon1 and A. Hajnal2
1 Bellcore,Morristown, NJ 07960,USA and Department ofMathematics, SacklerFacultyof
Exact Sciences,Tel AvivUniversity,Tel Aviv,Israel
2 Mathematical Institute ofthe Hungarian AcademyofSciences,Budapest,Hungary
Abstract.It is shown that anygraph on n verticescontainingno cliqueand no independent set on
t + 1verticeshas at least
2./( 2r2o~2t))
distinct induced subgraphs.
1. Introduction
All graphs considered here are finite, simple and undirected. G. always denotes a
graph on n vertices. For a graph G, let i(G) denote the total number of isomorphism
types of induced subgra_phs of G. We call i(G) the isomorphism number of G. Note
that i(G) = i(G), where G is the complement of G and that if G. has n vertices then
i(G.) > n, as G. contains an induced subgraph on m vertices for each I < m < n. An


Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics