University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Transversal cycle factors in multipartite graphs

## Transversal cycle factors in multipartite graphsAdd to your list(s) Download to your calendar using vCal - Amarja Kathapurkar, Birmingham
- Thursday 27 October 2022, 15:00-16:00
- LTC.
If you have a question about this talk, please contact Johannes Carmesin. A transversal Ck-factor in a k-partite graph G is a collection of vertex-disjoint copies of Ck in G such that each copy of Ck contains exactly one vertex from each vertex class, and such that every vertex of G belongs to some copy of Ck. Let G be a k-partite graph with vertex classes V1 , …, Vk each of size n. Suppose δ(G[Vi , Vi+1]) ≥ (1/2 \add 1/2k)n for each i in [k-1] and δ(G[V1 , Vk]) ≥ (1/2 \add 1/2k)n. We show that when k is even and n is sufficiently large, G contains a transversal Ck-factor. This resolves independent conjectures of Häggkvist and Fischer in the case when k is even. Furthermore, we show that when k is odd and n is sufficiently large, either G contains a transversal Ck-factor, or G is ‘close to’ being extremal. This is joint work with Richard Mycroft. This talk is part of the Combinatorics and Probability seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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