— Unstructured p2p and overlay network applications often require that a random graph be constructed, and that some form of random node selection take place over that graph. A ke...
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...
Abstract. The vertex cover problem is a classical NP-complete problem for which the best worst-case approximation ratio is 2− o(1). In this paper, we use a collection of simple g...
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...
Motivated by a problem that arises in the study of mirrored storage systems, we describe, for any fixed , > 0 and any integer d 2, explicit or randomized constructions of d-r...