A mobile agent (robot), modeled as a finite automaton, has to visit all nodes of a regular graph. How does the memory size of the agent (the number of states of the automaton) inf...
A clique in a graph G is a complete subgraph of G. A clique covering (partition) of G is a collection C of cliques such that each edge of G occurs in at least (exactly) one clique...
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 non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-subdivision into a K3,3-subdivision if it is possible, or else we obtain a partit...
We study the random graph Gn,λ/n conditioned on the event that all vertex degrees lie in some given subset S of the nonnegative integers. Subject to a certain hypothesis on S, the...