The achromatic number (G) of a graph G = (V, E) is the maximum k such that V has a partition V1, V2, . . . , Vk into independent sets, the union of no pair of which is independent...
The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d labels that is preserved only by a trivial automorphism. We prove that Cartesi...
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 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...
We consider the problem of periodic graph exploration by a finite automaton in which an automaton with a constant number of states has to explore all unknown anonymous graphs of a...