Consider random regular graphs of order n and degree d = d(n) 3. Let g = g(n) 3 satisfy (d-1)2g-1 = o(n). Then the number of cycles of lengths up to g have a distribution simila...
Brendan D. McKay, Nicholas C. Wormald, Beata Wysoc...
A set of paths joining a vertex y and a vertex set L is called (y, L)-fan if any two of the paths have only y in common, and its width is the number of paths forming it. In weight...
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...