Stability for Maximal Independent Sets

MAXIMAL INDEPENDENT SETS FOR THE PIXEL EXPANSION OF GRAPH ACCESS STRUCTURE

Given a graph G, a visual cryptography scheme based on the graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper we apply maximal independent sets of the grap...

Maximal Independent Sets for the Pixel Expansion of Graph Access Structure

 Abstract : A visual cryptography scheme based on a given graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper a maximal independent sets of the graph G was ...

Maximal k-independent sets in graphs

A subset of vertices of a graph G is k-independent if it induces in G a subgraph of maximum degree less than k. The minimum and maximum cardinalities of a maximal k-independent set are respectively denoted ik(G) and βk(G). We give some relations between βk(G) and βj(G) and between ik(G) and ij(G) for j 6= k. We study two families of extremal graphs for the inequality i2(G) ≤ i(G) + β(G). Finall...

Maximal Independent Sets and Separating Covers

In 1973, Katona raised the problem of determining the maximum number of subsets in a separating cover on n elements. The answer to Katona’s question turns out to be the inverse to the answer to a much simpler question: what is the largest integer which is the product of positive integers with sum n? We give a combinatorial explanation for this relationship, via Moon and Moser’s answer to a ques...

A Generalization of maximal independent sets