The Kruskal-Katona Theorem for Graphs
Combinatorics
2018-12-31 v2
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 also investigate cases where it is not. Finally we look at a useful technique for actually finding the numbers of complete subgraphs of a graph.
Keywords
Cite
@article{arxiv.1810.05704,
title = {The Kruskal-Katona Theorem for Graphs},
author = {Robert Cowen},
journal= {arXiv preprint arXiv:1810.05704},
year = {2018}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1809.03967