Consider random regular graphs of order n and degree d = d(n) 3. Let g = g(n) 3 satisfy (d-1)2g-1 = o(n). Then the number of cycles of lengths up to g have a distribution simila...
Brendan D. McKay, Nicholas C. Wormald, Beata Wysoc...
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edge...
A proper edge colouring of a graph is neighbour-distinguishing if for all pairs of adjacent vertices v, w the set of colours appearing on the edges incident with v is not equal to...
The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. We begin with a complete graph on n vertices and proceed to remove the ed...
We propose a new, recursive model to generate realistic graphs, evolving over time. Our model has the following properties: it is (a) flexible, capable of generating the cross pro...