We consider the isomorphism and canonization problem for 3-connected planar graphs. The problem was known to be L -hard and in UL ∩ coUL [TW08]. In this paper, we give a determin...
A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r-regular uniquely hamiltonian graphs when r > 22. This im...
Penny E. Haxell, Ben Seamone, Jacques Verstraë...
: Let G be a 3-connected planar graph and G∗ be its dual. We show that the pathwidth of G∗ is at most 6 times the pathwidth of G. We prove this result by relating the pathwidth...
The maximum independent set problem is NP-complete for graphs in general, but becomes solvable in polynomial time when restricted to graphs in many special classes. The problem is ...
We study problems of reconguration of shortest paths in graphs. We prove that the shortest reconguration sequence can be exponential in the size of the graph and that it is NP-hard...