Binary Polyhedral Groups and Euclidean Diagrams.
Bipartite coverings and the chromatic number.
Bipartite diametrical graphs of diameter 4 and extreme orders.
Bipartite graphs that are not circle graphs
The following result is proved: if a bipartite graph is not a circle graph, then its complement is not a circle graph. The proof uses Naji’s characterization of circle graphs by means of a linear system of equations with unknowns in .At the end of this short note I briefly recall the work of François Jaeger on circle graphs.
Bipartite intersection graphs
Bipartite knots
We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology, thus answering in the positive the question raised in 1987 by J. Przytycki.
Bipartite toughness and -factors in bipartite graphs.
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....
Biplanes.
Biregular edge-symmetric graphs
Block decomposition approach to compute a minimum geodetic set
In this paper, we develop a divide-and-conquer approach, called block decomposition, to solve the minimum geodetic set problem. This provides us with a unified approach for all graphs admitting blocks for which the problem of finding a minimum geodetic set containing a given set of vertices (g-extension problem) can be efficiently solved. Our method allows us to derive linear time algorithms for the minimum geodetic set problem in (a proper superclass of) block-cacti and monopolar chordal graphs....
Block distance matrices.
Block triangular preconditioners for -matrices and Markov chains.
Block-closed subgraphs and q-partitions of graphs
Bonferroni-Galambos inequalities for partition lattices.
Boolean differential operators
We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.
Boolean graphs
Boolean matrices ... neither Boolean nor matrices
Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.
Bootstrap clustering for graph partitioning
Given a simple undirected weighted or unweighted graph, we try to cluster the vertex set into communities and also to quantify the robustness of these clusters. For that task, we propose a new method, called bootstrap clustering which consists in (i) defining a new clustering algorithm for graphs, (ii) building a set of graphs similar to the initial one, (iii) applying the clustering method to each of them, making a profile (set) of partitions, (iv) computing a consensus partition for this profile,...