This thesis concerns the relationship between four graph invariants: ω, χf, χ, and∆. These are
the clique number, the fractional chromatic number, the chromatic number, and the …

The subject of this work is the study of LS+-perfect graphs defined as those graphs G for
which the stable set polytope STAB (G) is achieved in one iteration of Lovász–Schrijver PSD …

Let Mp, q the set of all 0/1-matrices with p rows and q columns. If you let a permutation group
operate on the columns of the elements of Mp, q, then Mp, q can be partitioned by a set of …

The total matching polytope generalizes the stable set polytope and the matching polytope.
In this paper, we first propose new facet-defining inequalities for the total matching polytope …

We introduce a new facet-generating procedure for the stable set polytope, based on
replacing (k− 1)-cliques with certain k-partite graphs, which subsumes previous procedures …

A total matching of a graph G=(V, E) is a subset of G such that its elements, ie vertices and
edges, are pairwise not adjacent. In this context, the Total Matching Problem calls for a total …

The stable set polytope is a fundamental object in combinatorial optimization. Among the
many valid inequalities that are known for it, the clique-family inequalities play an important …

The second author's (BAR) ω, Δ, χ conjecture proposes that every graph satisfies. In this
article, we prove that the conjecture holds for all claw‐free graphs. Our approach uses the …

Fuzzy antihat graphs are graphs obtained as 2-clique-bond compositions of fuzzy line
graphs with three different types of three-cliqued graphs. By the decomposition theorem of …

Abstract In [6], Edmonds provided the first complete description of the polyhedron associated
with a combinatorial optimization problem: the matching polytope. As the matching problem …