In this paper we study some connectivity augmentation problems. Given a connected graph G with some desirable property, we want to make G 2-vertex connected (or 2-edge connected) ...
We use transfer matrix methods to determine bounds for the numbers of legal Go positions for various numbers of players on some planar lattice graphs, including square lattice gra...
A dual-eulerian graph is a plane graph which has an ordering defined on its edge set which forms simultaneously an Euler circuit in the graph and an euler circuit in the dual grap...
For planar graphs, counting the number of perfect matchings (and hence determining whether there exists a perfect matching) can be done in NC [4, 10]. For planar bipartite graphs, ...
We provide polynomial time data reduction rules for Connected Dominating Set in planar graphs and analyze these to obtain a linear kernel for the planar Connected Dominating Set pr...