Atlantic Graph Theory Seminar: David Pike (Memorial)

Name: Atlantic Graph Theory Seminar: David Pike (Memorial)
Start: 2020-10-14T15:30:00-03:00
End: 2020-10-14T16:30:00-03:00
Location: Zoom seminar

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).

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Details

Date:: October 14, 2020
Time:: 3:30 pm - 4:30 pm
Event Category:: Atlantic Graph Theory Seminar
Website:: https://sites.google.com/view/atlanticgraphtheoryseminars/home

Venue

Zoom seminar

Organizers

: Danielle Cox
: Jason Brown