In one of fundamental works in combinatorial optimization, Edmonds gave a complete linear
description of the matching polytope. Matchings in a graph are equivalent to stable sets in its …

A spanning tree in a graph G where each node has distance at most 2 from a root node r is
called a 2-hop spanning tree. For given edge weights the 2-hop spanning tree problem is to …

Given a graph with nonnegative edge weights and a set D of node pairs, the 2‐path network
problem requires a minimum weight set of edges such that the induced subgraph contains a …

We deal with non-rank facets of the stable set polytope of claw-free graphs. We extend
results of Giles and Trotter [7] by (i) showing that for any nonnegative integer a there exists a …

A stable set in a graph G is a set of pairwise nonadjacent vertices. The problem of finding a
maximum weight stable set is one of the most basic ℕℙ-hard problems. An important …

In this thesis we focus our attention on the stable set polytope of claw-free graphs. This
problem has been open for many years and albeit all the efforts engaged during those last …

Webs and antiwebs are natural generalizations of odd holes and odd antiholes with circular
symmetry of their maximum cliques and stable sets. Webs and antiwebs turned out to play a …

Graphs with circular symmetry, called webs, are crucial for describing the stable set
polytopes of two larger graph classes, quasi-line graphs [8, 12] and claw-free graphs [7, 8] …

New results concerning the facial structure of set packing polyhedra are presented. In
particular, new methods are given to obtain facets from the subgraphs of the intersection …

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 …