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

Transversal cycle factors in multipartite graphs

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  • UserAmarja Kathapurkar, Birmingham
  • ClockThursday 27 October 2022, 15:00-16:00
  • HouseLTC.

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.

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