Colorings and orientations of matrices and graphs.
Colouring of cycles in the de Bruijn graphs
We show that the problem of finding the family of all so called the locally reducible factors in the binary de Bruijn graph of order k is equivalent to the problem of finding all colourings of edges in the binary de Bruijn graph of order k-1, where each vertex belongs to exactly two cycles of different colours. In this paper we define and study such colouring for the greater class of the de Bruijn graphs in order to define a class of so called regular factors, which is not so difficult to construct....
Combinatorial game theory foundations applied to digraph kernels.
Common consequents in directed graphs
Comparing a Cayley digraph with its reverse.
Competition hypergraphs of digraphs with certain properties II. Hamiltonicity
If D = (V,A) is a digraph, its competition hypergraph (D) has vertex set V and e ⊆ V is an edge of (D) iff |e| ≥ 2 and there is a vertex v ∈ V, such that . We give characterizations of (D) in case of hamiltonian digraphs D and, more general, of digraphs D having a τ-cycle factor. The results are closely related to the corresponding investigations for competition graphs in Fraughnaugh et al. [4] and Guichard [6].
Competition hypergraphs of digraphs with certain properties I. Strong connectedness
If D = (V,A) is a digraph, its competition hypergraph 𝓒𝓗(D) has the vertex set V and e ⊆ V is an edge of 𝓒𝓗(D) iff |e| ≥ 2 and there is a vertex v ∈ V, such that e = {w ∈ V|(w,v) ∈ A}. We tackle the problem to minimize the number of strong components in D without changing the competition hypergraph 𝓒𝓗(D). The results are closely related to the corresponding investigations for competition graphs in Fraughnaugh et al. [3].
Competitive colorings of oriented graphs.
Complétude en théorie sur graphes orientés
Complexes of Directed Trees of Complete Multipartite Graphs
Complexité de problèmes liés aux graphes sans circuit
Composantes préconservatives minimales d'un réseau de Petri : étude structurelle
Conditional resolvability in graphs: a survey.
Connected graphs containing a given connected graph as a unique greatest common subgraph.
Constructions over tournaments
We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments.
Convex independence and the structure of clone-free multipartite tournaments
We investigate the convex invariants associated with two-path convexity in clone-free multipartite tournaments. Specifically, we explore the relationship between the Helly number, Radon number and rank of such digraphs. The main result is a structural theorem that describes the arc relationships among certain vertices associated with vertices of a given convexly independent set. We use this to prove that the Helly number, Radon number, and rank coincide in any clone-free bipartite tournament. We...
Correction de mon article ’Sur le nombre des -cycles dans un tournoi’
Corrections to my papers “Some remarks on Menger's theorem” and “Alternating connectivity of digraphs”
Cotas inferiores para el QAP-árbol.
El QAP-Arbol es un caso especial del problema de asignación cuadrática en que los flujos distintos de cero forman un árbol. No se requiere ninguna condición para la matriz de distancias. En este artículo presentamos una formulación del QAP-Arbol como un problema de programación lineal entera. Basándonos en esta formulación hemos construido cuatro relajaciones lagrangianas distintas que nos permiten obtener una serie de cotas inferiores para este problema. Para resolver una de estas relajaciones,...
Counting unlabelled topologies and transitive relations.