Geodesic
Extending perfect matchings to Hamiltonian cycles in line graphs
Marién Abreu1 ; John Baptist Gauci2 ; Domenico Labbate1 ; Giuseppe Mazzuoccolo ; Jean Paul Zerafa3
1Università della Basilicata
2University of Malta
3University of Modena and Reggio Emilia
The electronic journal of combinatorics, Tome 28 (2021) no. 1
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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.
DOI : 10.37236/9143
Classification : 05C45, 05C70, 05C76
Mots-clés : perfect-matching-Hamiltonian property

Marién Abreu  1   ; John Baptist Gauci  2   ; Domenico Labbate  1   ; Giuseppe Mazzuoccolo    ; Jean Paul Zerafa  3

1 Università della Basilicata
2 University of Malta
3 University of Modena and Reggio Emilia 
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     author = {Mari\'en Abreu and John Baptist Gauci and Domenico Labbate and Giuseppe Mazzuoccolo and Jean Paul Zerafa},
     title = {Extending perfect matchings to {Hamiltonian} cycles in line graphs},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {1},
     doi = {10.37236/9143},
     zbl = {1456.05093},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9143/}
}
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Marién Abreu; John Baptist Gauci; Domenico Labbate; Giuseppe Mazzuoccolo; Jean Paul Zerafa. Extending perfect matchings to Hamiltonian cycles in line graphs. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/9143

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