We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs. We show that this problem is NP-complete in planar graphs, even if they a...
We first show that for any bipartite graph H with at most five vertices, there exists an on-line competitive algorithm for the class of H-free bipartite graphs. We then analyze th...
We show that there is a constant > 0 such that, for any set P of n 5 points in general position in the plane, a crossing-free geometric graph on P that is chosen uniformly at...
We present an experimental evaluation of an approximate distance oracle recently suggested by Thorup [1] for undirected planar graphs. The oracle uses the existence of graph separa...
We prove a lower bound of 0.3288 n 4¡ for the rectilinear crossing number cr(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadril...