Title:  Closed trail decompositions of complete equipartite graphs

Speaker:  Andrea Burgess (University of Ottawa)

Abstract:  The complete equipartite graph $K_m * \overline{K_n}$ has $mn$
vertices which are partitioned into $m$ parts, each of size $n$, with two
vertices adjacent if and only if they are not in the same part.  The final
determination of necessary and sufficient conditions for decomposition of
$K_m$ and $K_m * \overline{K_2}$ into cycles of fixed length was made by
Alspach, Gavlas and \v{S}ajna, while necessary and sufficient conditions
for decomposition of these graphs into closed trails of arbitrary lengths
were proven by Balister.  Since the appearance of these results, much
focus has shifted towards the corresponding decomposition problems for
complete equipartite graphs in general.  In this talk, we consider
decomposition of $K_m * \overline{K_n}$ into closed trails in the case
that all trails are of the same length.  In particular, we give necessary
and sufficient conditions for the existence of a decomposition of $K_m *
\overline{K_n}$ into closed trails of length $k$.