A graph admitting a perfect matching is said to have the Perfect-Matching-Hamiltonian property if each one of its perfect matchings can be extended to a Hamiltonian cycle of the graph. This property was first introduced by Las Vergnas and Häggkvist in the 1970s, a decade after Ore proved one of the most well-known results regarding Hamiltonicity. The main scope of these lectures is to introduce the above property and to take a comprehensive look at results in this area. Open problems and ideas for future work shall also be discussed.
CALENDAR ZOOM MEETINGS (please write to giuseppe.mazzuoccolo@univr.it to ask the link):
-July 8th (prerecorded lecture)
-July 18th (live 9.30-12.00)
-July 20th (live 9.30-12.00)
-July 25th (live 9.30-12.00)
-July 27th (live 9.30-12.00)
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