On the Conduciveness of Random Network Graphs for Maximal Assortative or Maximal Dissortative Matching

On the Conduciveness of Random Network Graphs for Maximal Assortative or Maximal Dissortative Matching

A maximal matching of a graph is the set of edges such that the addition of an edge to this set violates the property of matching (i.e., no two edges of the matching share a vertex). We use the notion of assortative index (ranges from -1 to 1) to evaluate the extent of similarity of the end vertices constituting the edges of a matching. A maximal matching of the edges whose assortative index is...

Maximal Inequalities for Associated Random Variables

In a celebrated work by Shao [13] several inequalities for negatively associated random variables were proved. In this paper we obtain some maximal inequalities for associated random variables. Also we establish a maximal inequality for demimartingales which generalizes and improves the result of Christofides [4].

Line graphs associated to the maximal graph

Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...

Random maximal H-free graphs

Spanning Maximal Planar Subgraphs of Random Graphs

We study the threshold for the existence of a spanning maximal planar subgraph in the random graph Gn . We show that it is very near p = ~TTOWe also discuss the threshold for the existence of a spanning maximal outerplanar subgraph. This is very near