—Symmetry breaking is a fundamental operation in distributed computing. It has applications to important problems such as graph vertex and edge coloring, maximal independent sets...
In this paper, we propose a simple and natural randomized algorithm to embed a tree T in a given graph G. The algorithm can be viewed as a "self-avoiding tree-indexed random ...
Given a distribution of pebbles on the vertices of a graph G, a pebbling move takes two pebbles from one vertex and puts one on a neighboring vertex. The pebbling number (G) is th...
David P. Bunde, Erin W. Chambers, Daniel W. Cranst...
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...
We consider edge-coloured complete graphs. A path or cycle Q is called properly coloured (PC) if any two adjacent edges of Q differ in colour. Our note is inspired by the followi...