More Cases Where the Kruskal-Katona Bound is Tight

Abstract

In graph theory, knowing the number of complete subgraphs with r vertices that a graph g has, limits the number of its complete subgraphs with s vertices, for s > r. A useful upper bound is provided by the Kruskal-Katona theorem, but this bound is often not tight. In this note, we add to the known cases where this bound is tight and begin an investigation of tight bounded graph sequences.