Graph Products with Small Cycle Double Covers

Document Type

Presentation Abstract

Presentation Date

9-12-2002

Abstract

A cycle double cover of a graph G is a collection of cycles, C, such that every edge of G lies in precisely two cycles of C. The Small Cycle Double Cover (SCDC) Conjecture, proposed by J.A. Bondy, asserts that every simple bridgeless graph on n vertices has a cycle double cover with at most n-1 cycles, and is a strengthening of the well-known Cycle Double Cover (CDC) Conjecture.

Both the CDC Conjecture and the SCDC Conjecture have been verified for various classes of graphs, but remain open in general. The graphs for which that SCDC Conjecture has been verified all have well defined structural properties that play an important role. The structure that is inherent in graph products makes such graphs ideal special cases for which to verify the SCDC Conjecture. There are various graph products that can be considered, and in this talk I will describe some results and techniques for proving the SCDC Conjecture for certain graph products.

This talk will be accessible to a general mathematics audience: all relevant terms will be defined, and proofs will be illustrated with examples. This is joint work with R.J. Nowakowski (Dalhousie University).

Additional Details

Thursday, 12 September 2002
4:10 p.m. in Math 109
Coffee/treats at 3:30 p.m. Math 104 (Lounge)

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