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Atlantic Graph Theory Seminar: David Pike (Memorial)

October 14, 2020 @ 3:30 pm - 4:30 pm

Perfect 1-Factorisations

A matching in a graph G is a subset M \subseteq E(G) of the edge set of G such that no two edges of M share a vertex. A 1-factor of a graph G is a matching F in which every vertex of G is in one of the edges of F. If G is a \Delta-regular graph of even order then we can ask whether G admits a 1-factorisation, namely a partition of its edge set into \Delta 1-factors.

Suppose that F_1, F_2, \ldots, F_\Delta are the 1-factors of a 1-factorisation \cal F of a \Delta-regular graph G. If, for each 1 \leq i < j \leq \Delta, the union F_i \cup F_j yields a Hamilton cycle in G, then we say that \cal F 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 K_{56}.

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).


October 14, 2020
3:30 pm - 4:30 pm
Event Category:


Zoom seminar


Danielle Cox
Jason Brown