We prove that the crossing number of a graph decays in a “continuous fashion” in the following sense. For any ε > 0 there is a δ > 0 such that for n sufficiently large...
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular g...
The crossing number cr(G) of a graph G is the minimum number of crossings over all drawings of G in the plane. In 1993, Richter and Thomassen [RT93] conjectured that there is a co...