We prove that for a graph G = (V,E) without bad K4 subdivision, and for b ∈ Z ∪E + , the b-stable set polytope is determined by the system of constraints determined by the vertices, edges and odd circuits. We also prove that this system is totally dual integral. This relates to t-perfect graphs. Let G = (V,E) be a graph and let b ∈ ZV ∪E + . Then a b-stable set in G is a vector x ∈ Z+ satisfyin...

Let G be an n-node graph without two disjoint odd cycles. The algorithm of Artmann, Weismantel and Zenklusen (STOC’17) for bimodular integer programs can used to find a maximum weight stable set in strongly polynomial time. Building on structural results characterizing sufficiently connected graphs cycles, we construct size- $$O(n^2)$$ extended formulation the polytope G.

The following type of problem arises in practice: in a node-weighted graph G, find a minimum weight node set that satisfies certain conditions and, in addition, induces a perfectly matchable subgraph of G. This has led us to study the convex hull of incidence vectors of node sets that induce perfectly matchable subgraphs of a graph G, which we call the perfectly matchable subgraph polytope of G...

polytope Abstract polytope November, 2013 – p. 2 Abstract polytope Abstract polytope −→ combinatorial generalization of convex polytopepolytope Abstract polytope −→ combinatorial generalization of convex polytope November, 2013 – p. 2 Abstract polytope Abstract polytope −→ combinatorial generalization of convex polytopepolytope Abstract polytope −→ combinatorial generalization of convex polytop...

Objective(s): The results of studies on vaccine development for foot-and-mouth disease (FMD) virus show that the use of inactivated vaccines for FMD virus is not completely effective. Novel vaccinations based on immuno-dominant epitopes have been shown to induce immune responses. Furthermore, for safety of immunization, access to efficient adjuvants against FMD virus seems to be critical.Materi...

An object representation scheme which allow_ fast Eucltdea,7 distance cal,:vlatu_rz is prese_ted. The object model eztends the polytope model by representLny objects as the convez hull of a finite set of spheres. An algorithm for calculating distances between objects is developed which is linear in the total number of spheres specifying the two objects.

We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.