Longest cycles in k-connected graphs with given independence number

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Abstract

The Chvátal–Erdős Theorem states that every graph whose connectivity is at least its independence number has a spanning cycle. In 1976, Fouquet and Jolivet conjectured an extension: If G is an n-vertex k-connected graph with independence number a, and ak, then G has a cycle with length at least k(n+ak)a. We prove this conjecture.

Keywords

Fouquet–Jolivet Conjecture
Circumference
Chvátal–Erdős Theorem
Connectivity
Independence number

Cited by (0)

1

Research partially supported by the Korean Research Foundation (MOEHRD, Basic Research Promotion Fund), grant KRF-2005-C00003.

2

Research partially supported by the National Security Agency under Award No. H98230-10-1-0363.