Airy phenomena and analytic combinatorics of connected graphs.
Almost all trees have an even number of independent sets.
An enumeration theorem for rooted graphs
An extremal property of Turán graphs.
An improved inductive definition of two restricted classes of triangulations of the plane
An inversion formula, matrix functions, combinatorial identities and graphs
Analytical enumeration of circulant graphs with prime-squared number of vertices.
Applications harmoniques entre graphes finis et un théorème de superrigidité
Nous définissons une ntoion d’énergie pour des applications entre deux graphes métriques finis et cherchons à minimiser l’énergie au sein d’une classe d’homotopie. Nous démontrons des théorèmes d’existence et d’unicité analogues à ceux de Eells-Sampson et de Hartman pour les applications harmoniques à valeurs dans les variétés à courbure négative ou nulle. Nous montrons également une propriété de stabilité des applications minimisantes par rapport aux revêtements de degré fini à la source. Une application...
Arbres binaires de recherche : propriétés combinatoires et applications
Asymptotic comparison of two constructions for large digraphs of given degree and diameter
We compare the asymptotic growth of the order of the digraphs arising from a construction of Comellas and Fiol when applied to Faber-Moore digraphs versus plainly the Faber-Moore digraphs for the corresponding degree and diameter.
Asymptotic enumeration of dense 0-1 matrices with equal row sums and equal column sums.
Asymptotic enumeration of labelled graphs by genus.
Asymptotic expansions for the coefficients of analytic generating functions.
Asymptotics for the probability of connectedness and the distribution of number of components.
Automatic enumeration of regular objects.
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....