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Graph Theory and Combinatorics Seminar: Weighted Turan Numbers and Maximum Crossing Numbers of Trees

Event Type
245 Altgeld Hall
Sep 7, 2021   1:00 pm  
Sean English (UIUC)
Sean English

Abstract: In extremal graph theory, the most natural question to consider involves finding the most edges in an n-vertex graph that does not contain any copy of some small forbidden graph F. We will explore a generalization of this to edge weighted graphs in which the edge weights are induced by a vertex weighting according to some rule. We will solve this problem for cliques when the rule involves weighting each edge by the product or the minimum of the weights of the endpoints.

The main motivation for the study of such problems is in applications to other combinatorial problems. In particular, we will use the product weighting to solve an extremal problem in which the n-vertex host graph is not complete, and we will use the minimum edge weighting to solve a problem involving the maximum rectilinear crossing number of trees.

This project was joint work with Patrick Bennett and Maria Talanda-Fisher.

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