The aim of this paper is to give a coherent account of the problem of constructing cubic graphs with large girth. There is a well-defined integer Î¼0(g), the smallest number of vertices for which aâ€¦ (More)

A proof that a concept is learnable provided the Vapnik-Chervonenkis dimension is finite is given. The proof is more explicit than previous proofs and introduces two new parameters which allow boundsâ€¦ (More)

The â€˜dollar gameâ€™ represents a kind of diffusion process on a graph. Under the rules of the game some configurations are both stable and recurrent, and these are known as critical configurations. Theâ€¦ (More)

The critical group of a graph is an abelian group that arises in several contexts, and there are some similarities with the groups that are used in cryptography. We construct a family of graphs withâ€¦ (More)

There are many types of activity which are commonly known as â€˜learningâ€™. Here, we shall discuss a mathematical model of one such process, known as the the â€˜probably approximately correctâ€™ (or PAC)â€¦ (More)

The chromatic polynomials considered in this paper are associated with graphs constructed in the following way. Take n copies of a complete graph Kb and, for i = 1, 2, . . . , n, join each vertex inâ€¦ (More)