Article

Hamilton and long cycles in t-tough graphs with $t>1$

February 2012
Mathematical Problems of Computer Science

DOI:10.51408/1963-0032

Authors:

Zhora Nikoghosyan

Institute for Informatics and Automation Problems of the National Academy of Sciences, Yerevan, Armenia

It is proved that if G is a t-tough graph of order n and minimum degree

\delta

with

t>1

then either G has a cycle of length at least

\min\{n,2\delta+4\}

or G is the Petersen graph.

ResearchGate has not been able to resolve any citations for this publication.

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Jun 1999
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In this article, we establish bounds for the length of a longest cycle C in a 2-connected graph G in terms of the minimum degree δ and the toughness t. It is shown that C is a Hamiltonian cycle or |C| ≥ (t + 1) δ + t. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 107127, 1999

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Last Updated: 05 Dec 2024