Speaker: Xavier Pérez Giménez, University of Nebraska-Lincoln

Title: Almost-perfect packings and Tuza's conjecture in the random geometric graph

Abstract: The triangle packing number nu(G) of a graph G is the maximum size of a set of edge-disjoint triangles in G. Tuza conjectured that in any graph G there exists a set of at most 2nu(G) edges intersecting every triangle in G. In a recent work together with Bennett, Cushman and Dudek, we show that Tuza's conjecture holds in the random geometric graph for a large range of densities. We also study the problem of covering almost all edges of the random geometric graph with edge-disjoint copies of some fixed graph F. In particular, we show the existence of almost-perfect packings for an infinite family of F. In this talk, I will give a gentle overview of the problem and the main ideas in the proofs.

Everyone is welcome on zoom (link below), or at Dal in room Chase 227.

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https://us02web.zoom.us/j/88013261876?pwd=XGocyHqvseXY8metPztPoSuulEEejX.1