On the Hamilton-Waterloo problem for a class of Cayley graphs

Tommaso Traetta
Ryerson University, Toronto (ON) Canada

PDF

Minisymposium: GENERAL SESSION TALKS

Content: The Hamilton--Waterloo problem HWP($\Gamma; m,n; \alpha$, $\beta$) asks for a factorization of the simple graph $\Gamma$ into $\alpha$ $C_m$--factors and $\beta$ $C_n$--factors. The classic version of the problem, that is, the case in which $\Gamma$ is the complete graph is still open, although it has been the subject of an extensive research activity. In this talk, I will consider the Cayley graph $C_m[n]=Cay(\mathbb{Z}_{m}\times \mathbb{Z}_{n}, S)$ with connection set $S=\{1,-1\}\times \mathbb{Z}_{n}$ and present an almost complete solution to HWP($C_m[n]; m,n; \alpha,\beta$) with $m$ and $n$ odd. Andrea Burgess will show how this result can be used to make progress on the classic problem. This is joint work with Andrea Burgess and Peter Danziger.

Back to all abstracts