Oberlin College and Conservatory

Proper 3-Colorings of Arbitrarily Large Cycles and Hypercubes, by Emily Cairncross ’21, Math Major

Wednesday, May 5 at 1:00pm to 1:20pm

Virtual Event

In this talk, we look at two families of graphs, cycles and hypercubes, and compare how their sets of proper 3-colorings differ as the graphs get arbitrarily large. In particular, we find the probability of pairs of vertices at various distances being the same color in order to understand the range and scale of interactions between them. As we look at larger and larger cycles, larger and larger hypercubes, patterns begin to emerge. While the colors of vertices fixed fractions of the cycle away from each other are independent, a random 3-coloring of the hypercube is essentially a 2-coloring. This models how local constraints can propagate very differently through different kinds of networks.

Please contact mathematics@oberlin.edu for the Zoom link to this event.

Sponsored by the Mathematics Honors Lecture Series

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Virtual Events


Academic, Mathematics



Contact Person

Terri Pleska, Administrative Assistant

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