The main aim of this short paper is to answer the following question. Given a fixed graph H, for which values of the degree d does a random d-regular graph on n vertices contain ...
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...
We consider random walks on two classes of random graphs and explore the likely structure of the vacant set viz. the set of unvisited vertices. Let (t) be the subgraph induced by ...
We present k-Flipper, a graph transformation algorithm that transforms regular undirected graphs. Given a path of k +2 edges it interchanges the end vertices of the path. By defin...
Let G be a fixed connected multigraph with no loops. A random n-lift of G is obtained by replacing each vertex of G by a set of n vertices (where these sets are pairwise disjoint)...
Catherine S. Greenhill, Svante Janson, Andrzej Ruc...