We describe the first algorithms to compute minimum cuts in surface-embedded graphs in near-linear time. Given an undirected graph embedded on an orientable surface of genus g, w...
It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a cho...
In the 1960's, Tutte presented a decomposition of a 2-connected finite graph into 3-connected graphs, cycles and bonds. This decomposition has been used to reduce problems on...
We consider the problem of coloring a planar graph with the minimum number of colors so that each color class avoids one or more forbidden graphs as subgraphs. We perform a detail...
Hajo Broersma, Fedor V. Fomin, Jan Kratochví...
We give tight bounds on the parallel complexity of some problems involving random graphs. Speci cally, we show that a Hamiltonian cycle, a breadth rst spanning tree, and a maximal...