Problemas aditivos y grafos de Cayley.
Problemas da teoria dos grafos e a sua relação com os problemas da cobertura e da partição de um conjunto
Problème de la bipartition minimale d'un graphe
Problèmes ouverts. Représentation graphique d'un graphe
Problems from the world surrounding perfect graphs
Problems in algebraic combinatorics.
Problems of Distance Geometry and Convex Properties of Quadratic Maps.
Problems on fully irregular digraphs
Problems on stars in complete graphs.
Problems remaining NP-complete for sparse or dense graphs
For each fixed pair α,c > 0 let INDEPENDENT SET () and INDEPENDENT SET () be the problem INDEPENDENT SET restricted to graphs on n vertices with or edges, respectively. Analogously, HAMILTONIAN CIRCUIT () and HAMILTONIAN PATH () are the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted to graphs with edges. For each ϵ > 0 let HAMILTONIAN CIRCUIT (m ≥ (1 - ϵ)(ⁿ₂)) and HAMILTONIAN PATH (m ≥ (1 - ϵ)(ⁿ₂)) be the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted...
Procédure automatique d'examen de dossiers fondée sur une segmentation trichotomique en présence de critères multiples
Processes on unimodular random networks.
Product rosy labeling of graphs
In this paper we describe a natural extension of the well-known ρ-labeling of graphs (also known as rosy labeling). The labeling, called product rosy labeling, labels vertices with elements of products of additive groups. We illustrate the usefulness of this labeling by presenting a recursive construction of infinite families of trees decomposing complete graphs.
Productive and inductive constructions of graphs
Products Of Digraphs And Their Competition Graphs
If D = (V, A) is a digraph, its competition graph (with loops) CGl(D) has the vertex set V and {u, v} ⊆ V is an edge of CGl(D) if and only if there is a vertex w ∈ V such that (u, w), (v, w) ∈ A. In CGl(D), loops {v} are allowed only if v is the only predecessor of a certain vertex w ∈ V. For several products D1 ⚬ D2 of digraphs D1 and D2, we investigate the relations between the competition graphs of the factors D1, D2 and the competition graph of their product D1 ⚬ D2.
Products of Geodesic Graphs and the Geodetic Number of Products
Given a connected graph and a vertex x ∈ V (G), the geodesic graph Px(G) has the same vertex set as G with edges uv iff either v is on an x − u geodesic path or u is on an x − v geodesic path. A characterization is given of those graphs all of whose geodesic graphs are complete bipartite. It is also shown that the geodetic number of the Cartesian product of Km,n with itself, where m, n ≥ 4, is equal to the minimum of m, n and eight.
Proof of a conjectured three-valued family of Weil sums of binomials
We consider Weil sums of binomials of the form , where F is a finite field, ψ: F → ℂ is the canonical additive character, , and . If we fix F and d, and examine the values of as a runs through , we always obtain at least three distinct values unless d is degenerate (a power of the characteristic of F modulo ). Choices of F and d for which we obtain only three values are quite rare and desirable in a wide variety of applications. We show that if F is a field of order 3ⁿ with n odd, and with...
Proof of Simoes-Pereira's conjectures on locally k-degenerate graphs.
Proof of the conjecture for large .
Propagation of mean degrees.