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DMS Colloquium – L. Berman: “Constructing snarks with rotationally symmetric drawings”

February 16 @ 1:00 PM - 2:00 PM

“Constructing snarks with rotationally symmetric drawings” – presented by Leah Berman, UAF Department of Mathematics and Statistics.

ABSTRACT: A snark is a cubic graph (every vertex is incident with three edges) where four colors are required to color the edges of the graph so that every vertex is incident with differently-colored edges. For example, the 5-prism (two pentagons with corresponding vertices joined by an edge) can be edge-colored with three colors, but the Petersen Graph (a pentagon and a pentagram, with corresponding vertices joined with an edge), you quickly reach a contradiction: the Petersen graph requires four colors to properly edge-color the graph—it is the smallest snark.
In this talk, I will give a little history of snark-hunting, and then describe construction methods to construct new infinite families of snarks that can be drawn with m-fold rotational symmetry. In contrast to previous methods, one of the new infinite families of snarks is constructed using building blocks that are not themselves snarks!
The talk will be accessible to undergraduates, and many pretty pictures will be provided.

A flier with additional information is attached (click on “more details” below and then on the attachment link).

Contact: Leah Berman, lwberman@alaska.edu


February 16
1:00 PM - 2:00 PM
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