Hamiltonicity, independence number, and pancyclicity
Combinatorics
2011-11-09 v2
Abstract
A graph on n vertices is called pancyclic if it contains a cycle of length l for all 3 \le l \le n. In 1972, Erdos proved that if G is a Hamiltonian graph on n > 4k^4 vertices with independence number k, then G is pancyclic. He then suggested that n = \Omega(k^2) should already be enough to guarantee pancyclicity. Improving on his and some other later results, we prove that there exists a constant c such that n > ck^{7/3} suffices.
Keywords
Cite
@article{arxiv.1104.3334,
title = {Hamiltonicity, independence number, and pancyclicity},
author = {Choongbum Lee and Benny Sudakov},
journal= {arXiv preprint arXiv:1104.3334},
year = {2011}
}