Contributions to the Theory of Colourings, Graph Minors, and Independent Sets Second Edition

INDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS

Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$,  if no two vertices of $S$ are adjacent.The  independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.

Very rapidly mixing Markov Chains for 2Δ-colourings and for independent sets in a graph with maximum degree 4

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 ...

Extending partial 3-colourings in a planar graph

Let D be a disc, and let X be a finite subset of vertices on the boundary of D. An essential part of the proof of the four colour theorem is the fact that many sets of 4-colourings of X do not arise from the proper 4-colourings of any graph drawn in D. In contrast to this, we show that every set of 3-colourings of X arises from the proper 3-colourings of some graph drawn in D.