Maximizing Cliques in Shellable Clique Complexes

Abstract

In extremal graph theory, the problem of finding the elements of a given class of graphs which contain the most cliques traces its routes back to Turán's famous theorem. We consider the implications of the connectivity property of simplicial complexes known as shellability on clique complexes associated with graphs. In this paper, we find the graphs which maximize cliques among all graphs on $n$ vertices with $\Delta (G)\le r$ that have shellable clique complexes.

18 pages, pre-print