Baxter permutations and plane bipolar orientations.
Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees.
Bijective counting of tree-rooted maps and shuffles of parenthesis systems.
Bipartite-uniform hypermaps on the sphere.
Bipartition Polynomials, the Ising Model, and Domination in Graphs
This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting representations, for instance as a sum ranging over all spanning forests. As a consequence, the bipartition polynomial is a powerful tool for proving properties of other graph polynomials and graph invariants....
Bounds for the Number of Perfect Matchings in Hexagonal Systems