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Atlantic Graph Theory Seminar: David Pike (Memorial)
October 14, 2020 @ 3:30 pm - 4:30 pm
A matching in a graph is a subset of the edge set of such that no two edges of share a vertex. A 1-factor of a graph is a matching in which every vertex of is in one of the edges of . If is a -regular graph of even order then we can ask whether admits a 1-factorisation, namely a partition of its edge set into 1-factors.
Suppose that are the 1-factors of a 1-factorisation of a -regular graph . If, for each , the union yields a Hamilton cycle in , then we say that is a perfect 1-factorisation. We will discuss some of the history and properties of 1-factorisations, including the recent discovery of a perfect 1-factorisation of .
The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).