Vol. 10, No. 5, 2017

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The Hamiltonian problem and $t$-path traceable graphs

Kashif Bari and Michael E. O’Sullivan

Vol. 10 (2017), No. 5, 801–812
Abstract

The problem of characterizing maximal non-Hamiltonian graphs may be naturally extended to characterizing graphs that are maximal with respect to nontraceability and beyond that to t-path traceability. We show how t-path traceability behaves with respect to disjoint union of graphs and the join with a complete graph. Our main result is a decomposition theorem that reduces the problem of characterizing maximal t-path traceable graphs to characterizing those that have no universal vertex. We generalize a construction of maximal nontraceable graphs by Zelinka to t-path traceable graphs.

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Keywords
maximal non-hamiltonian, hamiltonian, graph theory, t-path traceable
Mathematical Subject Classification 2010
Primary: 05C45
Milestones
Received: 7 February 2016
Revised: 23 June 2016
Accepted: 24 July 2016
Published: 14 May 2017

Communicated by Ronald Gould
Authors
Kashif Bari
Department of Mathematics and Statistics
San Diego State University
San Diego, CA 92182
United States
Michael E. O’Sullivan
Department of Mathematics and Statistics
San Diego State University
San Diego, CA 92182
United States