Elsevier

Discrete Mathematics

Volume 342, Issue 7, July 2019, Pages 1919-1923
Discrete Mathematics

Note
A variation of a theorem by Pósa

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Abstract

A graph G is -hamiltonian if each linear forest F with edges contained in G can be extended to a hamiltonian cycle of G. 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: if a non--hamiltonian graph contains almost the maximum number of cliques, then it is a subgraph of one of two extremal graphs.

Keywords

Turán problem
Hamiltonian cycles
Extremal graph theory

Cited by (0)

1

Research supported in part by the Hungarian National Research, Development and Innovation Office NKFIH grant K116769, and by the Simons Foundation Collaboration Grant 317487.

2

Research is supported in part by NSF grant DMS-1600592 and grants 18-01-00353A and 16-01-00499 of the Russian Foundation for Basic Research .