A variation of a theorem by P\'osa
Combinatorics
2018-04-19 v2
Abstract
A graph is -hamiltonian if for any linear forest of with edges, can be extended to a hamiltonian cycle of . We give a sharp upper bound for the maximum number of cliques of a fixed size in a non--hamiltonian graph. Furthermore, we prove stability for the bound: if a non--hamiltonian graph contains almost the maximum number of cliques, then it must be a subgraph of one of two examples.
Cite
@article{arxiv.1804.05829,
title = {A variation of a theorem by P\'osa},
author = {Zoltan Furedi and Alexandr Kostochka and Ruth Luo},
journal= {arXiv preprint arXiv:1804.05829},
year = {2018}
}