We analyze a randomized version of the Brelaz heuristic on sparse random graphs. We prove that almost all graphs with average degree dp4:03; i.e., G?n; p ? d=n?; are 3-colorable a...
Consider an acyclic directed network G with sources S1, S2, . . . , Sl and distinct sinks R1, R2, . . . , Rl. For i = 1, 2, . . . , l, let ci denote the min-cut between Si and Ri....
We give a deterministic algorithm to find the minimum cut in a surface-embedded graph in near-linear time. Given an undirected graph embedded on an orientable surface of genus g,...
We prove the conjecture of Abbott and Katchalski that for every m ≥ 2 there is a positive constant λm such that S(Kd mn) ≥ λmnd−1 S(Kd−1 m ) where S(Kd m) is the length o...
A dominating set of a graph G = (V, E) is a subset V V of the nodes such that for all nodes v V , either v V or a neighbor u of v is in V . Several routing protocols in ad hoc ...
Alaa Eddien Abdallah, Thomas Fevens, Jaroslav Opat...