Atlantic Graph Theory Seminar: Andrea Burgess (UNB)

Mutually Orthogonal Cycle Systems

A $k$-cycle system of order $n$ is a set of $k$-cycles whose edges partition the edge set of $K_n$.  We say that two cycle systems $\mathcal{C}$ and $\mathcal{C}’$ are {\em orthogonal} if every cycle in $\mathcal{C}$ shares at most one edge with each cycle in $\mathcal{C}’$.  Orthogonal cycle systems arise naturally from simple Heffter arrays and biembeddings of cycle decompositions.

A collection of cycle systems is {\em mutually orthogonal} if any two of the systems are orthogonal.  In this talk, we give bounds on the number of mutually orthogonal $k$-cycle systems of order $n$ and provide constructions for sets of mutually orthogonal cyclic cycle systems.

This is joint work with Nicholas Cavenagh and David Pike.

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