Let F1, F2, . . . , Fk be graphs with the same vertex set V . A subset S V is a factor dominating set if in every Fi every vertex not in S is adjacent to a vertex in S, and a fac...
Peter Dankelmann, Michael A. Henning, Wayne Goddar...
A Graph Construction Game is a Maker-Breaker game. Maker and Breaker take turns in choosing previously unoccupied edges of the complete graph KN . Maker's aim is to claim a c...
In this paper we consider the problem of testing whether a graph is triangle-free, and more generally, whether it is H-free, for a fixed subgraph H. The algorithm should accept gr...
Noga Alon, Tali Kaufman, Michael Krivelevich, Dana...
We show that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. The proof uses an efficient algorithm which a.a.s. 3colours a random 4-regular ...
A solution to a problem of Erdos, Rubin and Taylor is obtained by showing that if a graph G is (a : b)-choosable, and c/d > a/b, then G is not necessarily (c : d)-choosable. Th...