We develop a new method for enumerating independent sets of a fixed size in general graphs, and we use this method to show that a conjecture of Engbers and Galvin holds for all bu...
: Let λ2(G) and τ(G) denote the second largest eigenvalue and the maximum number of edge-disjoint spanning trees of a graph G, respectively. Motivated by a question of Seymour on...
We produce an edge-coloring of the complete 3-uniform hypergraph on n vertices with eO( √ log log n) colors such that the edges spanned by every set of five vertices receive at...
In this paper we consider minors of ribbon graphs (or, equivalently, cellularly embedded graphs). The theory of minors of ribbon graphs differs from that of graphs in that contrac...