One of the most extensively researched real-world networks is the web graph. The web graph has vertices representing web pages, with edges corresponding to the links between pages. We describe someâ€¦ (More)

Several stochastic models were proposed recently to model the dynamic evolution of the web graph. We study the infinite limits of the stochastic processes proposed to model the web graph when timeâ€¦ (More)

A simple graph G has the neighbour-closed-co-neighbour property, or ncc property, if for all vertices x of G, the subgraph induced by the set of neighbours of x is isomorphic to the subgraph inducedâ€¦ (More)

Proteins are essential macromolecules of life that carry out most cellular processes. Since proteins aggregate to perform function, and since protein-protein interaction (PPI) networks model theseâ€¦ (More)

Meynielâ€™s conjecture is one of the deepest open problems on the cop number of a graph. It states that for a connected graph G of order n, c(G) = O( âˆš n). While largely ignored for over 20 years, theâ€¦ (More)

We consider the game of Cops and Robber played with infinitely many cops on countable graphs. We give a sufficient conditionâ€” the strongly 1-e.c. propertyâ€”for the cop number to be infinite. The copâ€¦ (More)

A graph is called n-existentially closed or n-e.c. if it satis/es the following adjacency property: for every n-element subset S of the vertices, and for every subset T of S, there is a vertex not inâ€¦ (More)