-valuations of graphs
Bipartite diametrical graphs of diameter 4 and extreme orders.
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.
Bounding the number of edges in permutation graphs.
Bounds for the number of meeting edges in graph partitioning
Let be a weighted hypergraph with edges of size at most 2. Bollobás and Scott conjectured that admits a bipartition such that each vertex class meets edges of total weight at least , where is the total weight of edges of size and is the maximum weight of an edge of size 1. In this paper, for positive integer weighted hypergraph (i.e., multi-hypergraph), we show that there exists a bipartition of such that each vertex class meets edges of total weight at least , where is the number...
Bounds for the rainbow connection number of graphs
An edge-coloured graph G is rainbow-connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow-connected. In this paper we show some new bounds for the rainbow connection number of graphs depending on the minimum degree and other graph parameters. Moreover, we discuss sharpness of some of these bounds.
Bounds of eigenvalues of -minor free graphs.
Bounds on the Signed 2-Independence Number in Graphs
Let G be a finite and simple graph with vertex set V (G), and let f V (G) → {−1, 1} be a two-valued function. If ∑x∈N|v| f(x) ≤ 1 for each v ∈ V (G), where N[v] is the closed neighborhood of v, then f is a signed 2-independence function on G. The weight of a signed 2-independence function f is w(f) =∑v∈V (G) f(v). The maximum of weights w(f), taken over all signed 2-independence functions f on G, is the signed 2-independence number α2s(G) of G. In this work, we mainly present upper bounds on α2s(G),...
Bounds on the Turán density of PG(3, 2).
Breaking symmetry on complete bipartite graphs of odd size.
Brève communication. Une caractérisation des graphes chromatiques minimaux sans sommet isolé
Brève communication. Une nouvelle méthode de marquage dans la recherche d'une chaîne de longueur maximale d'un arbre
Bridges and Hamiltonian circuits in planar graphs.