Title: Fractional decompositions and Latin square completion
| Speaker: | Peter Dukes |
| Affiliation: | University of Victoria |
| Zoom: | Contact Soffia Arnadottir |
Abstract:
It was shown recently by Delcourt and Postle that any sufficiently large graph $G$ of order $n$ with minimum degree at least $0.827n$ has a fractional triangle decomposition, i.e. an assignment of weights to the triangles in $G$ such that for every edge $e$, the total of all weights of triangles containing $e$ is exactly one.
This talk will consider the same problem in the $3$-partite setting. Using algebraic methods, we establish a minimum degree threshold for balanced $3$-partite graphs to admit a fractional triangle decomposition. Invoking the absorber work of Barber, K\"uhn, Lo, Osthus and Taylor, our threshold improves the status of the completion problem for sparse partial Latin squares of large order.
This is based on joint work with Flora Bowditch.