A quasi-kernel of a digraph D is an independent set Q⊆V(D) such that for every vertex v∈V(D)﹨Q, there exists directed path with one or two arcs from v to u∈Q. In 1974, Chvátal and Lovász proved has quasi-kernel. 1976, Erdős Székely conjectured sink-free D=(V(D),A(D)) size at most |V(D)|/2. this paper, we give new method show the conjecture holds generalization anti-claw-free digraphs. For any o...

We look at a different security property one might require of encryption, namely one-way security. The notion is natural and seems like a minimal requirement on an encryption scheme. It makes sense for both symmetric and public-key encryption schemes. To make the discussion more concrete, we look at the so-called “textbook” variant of the RSA encryption, and see how to pick keys in relation to ...

The minimum 3-way cut problem in an edge-weighted hypergraph is to find a partition of the vertices into 3 sets minimizing the total weight of hyperedges with at least two endpoints in two different sets. In this paper we present some structural properties for minimum 3-way cuts and design an O(dmn) algorithm for the minimum 3-way cut problem in hypergraphs, where n and m are the numbers of ver...