Let G be a graph with no three independent vertices. How many edges of G can be packed with edge-disjoint copies of Kk? More specifically, let fk(n, m) be the largest integer t s...
Abstract. We provide new tools, such as k-troikas and good subtreerepresentations, that allow us to give fast and simple algorithms computing branchwidth. We show that a graph G ha...
A graph is Y Y reducible if it can be reduced to isolated vertices by a sequence of series-parallel reductions and Y Y transformations. It is still an open problem to characterize...
Let ccl(G) denote the order of the largest complete minor in a graph G (also called the contraction clique number) and let Gn,p denote a random graph on n vertices with edge probab...
Given a graph on n vertices which is the union of two comparability graphs on the same vertex set, it always contains a clique or independent set of size n 1 3 . On the other hand...