Iain Moffatt

Learn More
Recently S. Chmutov introduced a generalization of the dual of a ribbon graph (or equivalently an embedded graph) and proved a relation between Bollobás and Riordan's ribbon graph polynomial of a ribbon graph and of its generalized duals. Here I show that the duality relation satisfied by the ribbon graph polynomial can be understood in terms of knot theory(More)
We find a number of new combinatorial identities for, and interpretations of evaluations of, the topological Tutte polynomials of Las Vergnas, L(G), and of and Bollobás and Riordan, R(G), as well as for the classical Tutte polynomial T (G). For example, we express R(G) and T (G) as a sum of chromatic polynomials, show that R(G) counts non-crossing graph(More)
This paper is dedicated to the memory of Michel Las Vergnas in gratitude for not only so much beautiful mathematics, but also many instances of very kind and insightful correspondence. Abstract. The Las Vergnas polynomial is an extension of the Tutte polynomial to cellularly embedded graphs. It was introduced by Michel Las Vergnas in 1978 as special case of(More)