En dos artículos, publicados en 1989, Balas y Ng dan una metodología para construir facetas del politopo de recubrimiento con coeficientes en {0, 1, 2}. Siguiendo esta metodología, en el presente artículo decimos cómo se contruyen facetas de dicho politopo con coeficientes en {0, 1, 2, 3}.
The class of DCT-graphs is a common generalization of the classes of almost claw-free and quasi claw-free graphs. We prove that every even (2p+1)-connected DCT-graph G is p-extendable, i.e., every set of p independent edges of G is contained in a perfect matching of G. This result is obtained as a corollary of a stronger result concerning factor-criticality of DCT-graphs.
By a result of McKenzie [4] finite directed graphs that satisfy certain connectivity and thinness conditions have the unique prime factorization property with respect to the cardinal product. We show that this property still holds under weaker connectivity and stronger thinness conditions. Furthermore, for such graphs the factorization can be determined in polynomial time.
A property of graphs is any isomorphism closed class of simple graphs. For given properties of graphs ₁,₂,...,ₙ a vertex (₁, ₂, ...,ₙ)-partition of a graph G is a partition V₁,V₂,...,Vₙ of V(G) such that for each i = 1,2,...,n the induced subgraph has property . The class of all graphs having a vertex (₁, ₂, ...,ₙ)-partition is denoted by ₁∘₂∘...∘ₙ. A property is said to be reducible with respect to a lattice of properties of graphs if there are n ≥ 2 properties ₁,₂,...,ₙ ∈ such that = ₁∘₂∘...∘ₙ;...
The Erdős-Faber-Lovász conjecture is the statement that every graph that is the union of n cliques of size n intersecting pairwise in at most one vertex has chromatic number n. Kahn and Seymour proved a fractional version of this conjecture, where the chromatic number is replaced by the fractional chromatic number. In this note we investigate similar fractional relaxations of the Erdős-Faber-Lovász conjecture, involving variations of the fractional chromatic number. We exhibit some relaxations that...
An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let [...] be an additive hereditary property of graphs. A [...] -edge-coloring of a simple graph is an edge coloring in which the edges colored with the same color induce a subgraph of property [...] . In this paper we present some results on fractional [...] -edge-colorings. We determine the fractional [...] -edge chromatic number for matroidal properties of graphs.