For all integers k 3, we give an O(n4 ) time algorithm for the problem whose instance is a graph G of girth at least k together with k vertices and whose question is "Does G...
In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on ...
Richard Kenyon, James Gary Propp, David Bruce Wils...
Abstract: A k-tree is a chordal graph with no (k + 2)-clique. An -treepartition of a graph G is a vertex partition of G into `bags,' such that contracting each bag to a single...
Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones....
The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the first part of the p...