Applying Lehman's theorems to packing problems
Mathematical Programming: Series A and B
The rank facets of the stable set polytope for claw-free graphs
Journal of Combinatorial Theory Series B
Polyhedral characterizations and perfection of line graphs
Discrete Applied Mathematics
Line graphs and forbidden induced subgraphs
Journal of Combinatorial Theory Series B
Stable Set Polytopes for a Class of Circulant Graphs
SIAM Journal on Optimization
Graphs and Hypergraphs
On non-rank facets of stable set polytopes of webs with clique number four
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
A construction for non-rank facets of stable set polytopes of webs
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Gear Composition of Stable Set Polytopes and G-Perfection
Mathematics of Operations Research
On non-rank facets of stable set polytopes of webs with clique number four
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Note: Facet-inducing web and antiweb inequalities for the graph coloring polytope
Discrete Applied Mathematics
Smoothed analysis of integer programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Gear composition and the stable set polytope
Operations Research Letters
On the facets of the stable set polytope of quasi-line graphs
Operations Research Letters
On the feedback vertex set polytope of a series-parallel graph
Discrete Optimization
2-clique-bond of stable set polyhedra
Discrete Applied Mathematics
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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 line graph. Also the neighborhood of any vertex in a line graph partitions into two cliques: graphs with this latter property are called quasi-line graphs. Quasi-line graphs are a subclass of claw-free graphs, and as for claw-free graphs, there exists a polynomial algorithm for finding a maximum weighted stable set in such graphs, but we do not have a complete characterization of their stable set polytope (SSP). In the paper, we introduce a class of inequalities, called clique-family inequalities, which are valid for the SSP of any graph and match the odd set inequalities defined by Edmonds for the matching polytope. This class of inequalities unifies all the known (non-trivial) facet inducing inequalities for the SSP of a quasi-line graph. We, therefore, conjecture that all the non-trivial facets of the SSP of a quasi-line graph belong to this class. We show that the conjecture is indeed correct for the subclasses of quasi-line graphs for which we have a complete description of the SSP. We discuss some approaches for solving the conjecture and a related problem.