We introduce a concept of dual consistency of systems of linear inequalities with full generality. We show that a cardinality constrained polytope is represented by a certain system of linear inequalities if and only if the systems of linear inequalities associated with the cardinalities are dual consistent. Typical dual consistent systems of inequalities are those which describe polymatroids, ...

In this paper, we investigate the communication cost of reproducing Einstein-Podolsky-Rosen (EPR) steering correlations arising from bipartite quantum systems. We characterize the set of bipartite quantum states which admits a local hidden state model augmented with c bits of classical communication from an untrusted party (Alice) to a trusted party (Bob). In case of one bit of information (c =...

in this paper, we introduce the notion of primal strong co-ideals and give some results involving them. it is shown thatsubtractive strong co-ideals are intersection of all primal strong co-ideals that contain them. also we prove that the representation of strong co-ideals as reduced intersections of primal strong co-ideals is unique.

A circular-arc hypergraph H is a hypergraph admitting an arc ordering, that is, a circular ordering of the vertex set V (H) such that every hyperedge is an arc of consecutive vertices. An arc ordering is tight if, for any two hyperedges A and B such that ∅ 6 = A ⊆ B 6= V (H), the corresponding arcs share a common endpoint. We give sufficient conditions for H to have, up to reversing, a unique a...

The enumeration of independent sets in graphs with various restrictions has been a topic of much interest of late. Let i(G) be the number of independent sets in a graph G and let it(G) be the number of independent sets in G of size t. Kahn used entropy to show that if G is an r-regular bipartite graph with n vertices, then i(G) ≤ i(Kr,r). Zhao used bipartite double covers to extend this bound t...

We investigate the class of vertex intersection graphs of paths on a grid, and specifically consider the subclasses that are obtained when each path in the representation has at most k bends (turns). We call such a subclass the Bk-VPG graphs, k ≥ 0. If the number k of bends is not restricted, then the VPG graphs are shown to be equivalent to the well-known class of string graphs, namely, the in...

In this paper, we introduce the notion of primal strong co-ideals and give some results involving them. It is shown thatsubtractive strong co-ideals are intersection of all primal strong co-ideals that contain them. Also we prove that the representation of strong co-ideals as reduced intersections of primal strong co-ideals is unique.

Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of  $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is conne...