Extending perfect matchings to Hamiltonian cycles in line graphs [article]

Marién Abreu, John Baptist Gauci, Domenico Labbate, Giuseppe Mazzuoccolo, Jean Paul Zerafa
2020 arXiv   pre-print
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.
more » ... related questions and open problems are proposed along the paper.
arXiv:1910.01553v2 fatcat:hlody5g6uzbjvpt7yufwu56zri