We consider the problem of constructing bounded-degree planar geometric spanners of Euclidean and unit-disk graphs. It is well known that the Delaunay subgraph is a planar geometri...
We investigate the following vertex percolation process. Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p = n-...
Catherine S. Greenhill, Fred B. Holt, Nicholas C. ...
d Abstract) Colin Cooper∗ , Martin Dyer† and Catherine Greenhill‡ We consider a simple Markov chain for d-regular graphs on n vertices, and show that the mixing time of this...
Colin Cooper, Martin E. Dyer, Catherine S. Greenhi...
Given a graph G and an integer k, two players alternatively color the edges of G using k colors so that adjacent edges get different colors. The game chromatic index g(G) is the m...
Andrew Beveridge, Tom Bohman, Alan M. Frieze, Oleg...
Abstract. We deal with two intimately related subjects: quasi-randomness and regular partitions. The purpose of the concept of quasi-randomness is to measure how much a given graph...