Short proofs on the matching polyhedron

On the cut polyhedron

The cut polyhedron cut(G) of an undirected graph G = (V,E) is the dominant of the convex hull of all its nonempty edge cutsets. After examining various compact extended formulations for cut(G), we study some of its polyhedral properties. In particular, we characterize all the facets induced by inequalities with right-hand side at most 2. These include all the rank facets of the polyhedron.

SHORT PROOFS ON Lr - DIFFERENTIABILITY 3

On quantum interactive proofs with short messages

This paper proves one of the open problems posed by Beigi, Shor and Watrous in [ToC, Volume 7, Article 7, pp. 101–117, 2011]. We consider quantum interactive proof systems where, in the beginning, the verifier and prover send messages to each other, with the combined length of all messages being at most logarithmic (in the input length); and at the end, the prover sends a polynomial-length mess...

Two short proofs on total domination

A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph γt (G) is the minimum size of a total dominating set. We provide a short proof of the result that γt (G) ≤ 2 3 n for connected graphs with n ≥ 3 and a short characterization of the extremal graphs.

Short Discreet Proofs

We show how to produce short proofs of theorems such that a distrusting Verifier can be convinced that the theorem is true yet obtains no information about the proof itself. The proofs are non-interactive provided that the quadratic residuosity bit commitment scheme is available to the Prover and Verifier. For typical applications, the proofs are short enough to fit on a floppy disk.