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...
Let C be a family of n compact connected sets in the plane, whose intersection graph G(C) has no complete bipartite subgraph with k vertices in each of its classes. Then G(C) has ...
The geometric simultaneous embedding problem asks whether two planar graphs on the same set of vertices in the plane can be drawn using straight lines, such that each graph is pla...
Sergio Cabello, Marc J. van Kreveld, Giuseppe Liot...
We present an O(n) time algorithm for simultaneous embedding of pairs of planar graphs on the O(n2 )×O(n2 ) grid, with at most three bends per edge, where n is the number of verti...
We present subexponential parameterized algorithms on planar graphs for a family of problems of the following shape: given a graph, find a connected (induced) subgraph with bounde...