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...
Let G be a graph with n vertices and independence number . Hadwiger's conjecture implies that G contains a clique minor of order at least n/. In 1982, Duchet and Meyniel prov...
We first prove that for any fixed k a cubic graph with few short cycles contains a Kk-minor. This is a direct generalisation of a result on girth by Thomassen. We then use this the...
In this paper, we present a Branch and Bound algorithm called QuickBB for computing the treewidth of an undirected graph. This algorithm performs a search in the space of perfect ...