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arXiv · 1508.05901

The Hamiltonian problem and $t$-path traceable graphs

Kashif Bari·Michael E. O'Sullivan
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Abstract

The problem of characterizing maximal non-Hamiltonian graphs may be naturally extended to characterizing graphs that are maximal with respect to non-traceability and beyond that to $t$-path traceability. We show how 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 non-traceable graphs by Zelinka to $t$-path traceable graphs.

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Kashif Bari, Michael E. O'Sullivan. 2015-08-24. The Hamiltonian problem and $t$-path traceable graphs. https://doi.org/10.2140/involve.2017.10.801

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