We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by O(27.55n ) = O(18...
A nonplanar graph G is near-planar if it contains an edge e such that G − e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from di...
The coefficient of fragmentability of a class of graphs measures the proportion of vertices that need to be removed from the graphs in the class in order to leave behind bounded s...
We show that the reachability problem for directed graphs that are either K3,3-free or K5-free is in unambiguous log-space, UL coUL. This significantly extends the result of Bour...
Abstract. We introduce the simultaneous representation problem, defined for any graph class C characterized in terms of representations, e.g. any class of intersection graphs. Two...