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Penny Haxell - Packing and covering triangles in dense graphs



PENNY HAXELL, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario  N2L 3G1, Canada
Packing and covering triangles in dense graphs


For a graph G, let $\nu(G)$ denote the maximum size of a set of pairwise edge-disjoint triangles in G, and $\tau(G)$ denote the minimum size of a set of edges C of G such that every triangle of G contains an edge from C. A conjecture of Tuza states that $\tau(G)\leq 2\nu(G)$ for every graph G. Some results on this conjecture will be presented, in particular that it is approximately true for dense graphs.



eo@camel.math.ca