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arXiv · 1910.01553

Extending perfect matchings to Hamiltonian cycles in line graphs

Marién Abreu·John Baptist Gauci·Domenico Labbate·Giuseppe Mazzuoccolo·Jean Paul Zerafa
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Abstract

A graph admitting a perfect matching has the Perfect-Matching-Hamiltonian property (for short the PMH-property) if each of its perfect matchings can be extended to a Hamiltonian cycle. In this paper we establish some sufficient conditions for a graph $G$ in order to guarantee that its line graph $L(G)$ has the PMH-property. In particular, we prove that this happens when $G$ is (i) a Hamiltonian graph with maximum degree at most $3$, (ii) a complete graph, or (iii) an arbitrarily traceable graph. Further related questions and open problems are proposed along the paper.

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Marién Abreu, John Baptist Gauci, Domenico Labbate, Giuseppe Mazzuoccolo, Jean Paul Zerafa. 2019-10-03. Extending perfect matchings to Hamiltonian cycles in line graphs. https://doi.org/10.37236/9143

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