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.
Boole's formula as a consequence of Lagrange's interpolating polynomial theorem.
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,...
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,...
Bootstrap percolation and diffusion in random graphs with given vertex degrees.
Borsuk-Ulam type theorems
A generalization of the theorem of Bajmóczy and Bárány which in turn is a common generalization of Borsuk's and Radon's theorem is presented. A related conjecture is formulated.
Bottom Schur functions.
Bound graph polysemy.
Boundary domination in graphs
Boundary of the union of rectangles in the plane
Given rectangles in a plane whose all sides belong to two perpendicular directions, an algorithm for the construction of the boundary of the union of those rectangles is shown in teh paper.
Bounded expansion in web graphs
In this paper we study various models for web graphs with respect to bounded expansion. All the deterministic models even have constant expansion, whereas the copying model has unbounded expansion. The most interesting case turns out to be the preferential attachment model --- which we conjecture to have unbounded expansion, too.
Bounded-degree graphs can have arbitrarily large slope numbers.
Bounded-degree graphs have arbitrarily large geometric thickness.
Bounding neighbor-connectivity of Abelian Cayley graphs
For the notion of neighbor-connectivity in graphs whenever a vertex is subverted the entire closed neighborhood of the vertex is deleted from the graph. The minimum number of vertices whose subversion results in an empty, complete, or disconnected subgraph is called the neighbor-connectivity of the graph. Gunther, Hartnell, and Nowakowski have shown that for any graph, neighbor-connectivity is bounded above by κ. Doty has sharpened that bound in abelian Cayley graphs to approximately (1/2)κ. The...
Bounding the complexity of simplicial group actions on trees.
Bounding the number of edges in permutation graphs.
Bounding the partition function of spin-systems.
Bounding the Rank of Certain Permutation Groups.
Bounds and inequalities for the Perron root of a nonnegative matrix. III: Bounds dependent on simple paths and circuits.