Bujtás Csilla: Tuza's Conjecture and further problems on edges and triangles

We will celebrate the 70th birthday of Zsolt Tuza.

Abstract: Zsolt Tuza posed the following conjecture more than 40 years ago: If a graph G does not contain more than k pairwise edge-disjoint triangles, then a set of at most 2k edges exists that cover all triangles in G. We discuss results related to this long-standing conjecture, concentrating on K_4-free graphs.

Based on a recent manuscript, we also consider problems concerning the minimum number of edges and triangles that cover all edges of a graph and the maximum size of an edge set that contains at most one edge from each triangle. (Coauthors: A. Davoodi, L. Ding, E. Győri, Zs. Tuza, and D. Yang)