We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the mo...
Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones....
In Graph Minors III, Robertson and Seymour write:"It seems that the tree-width of a planar graph and the tree-width of its geometric dual are approximately equal -- indeed, w...