Bucic, M; Jahn, E; Pokrovskiy, A; Sudakov, B; (2020) 2-factors with k cycles in Hamiltonian graphs. Journal of Combinatorial Theory, Series B , 144 pp. 150-166. 10.1016/j.jctb.2020.02.002.

Preview

Text 1905.09729.pdf - Accepted Version Download (420kB) | Preview

Abstract

A well known generalisation of Dirac’s theorem states that if a graph G on n ≥ 4k vertices has minimum degree at least n/2 then G contains a 2-factor consisting of exactly k cycles. This is easily seen to be tight in terms of the bound on the minimum degree. However, if one assumes in addition that G is Hamiltonian it has been conjectured that the bound on the minimum degree may be relaxed. This was indeed shown to be true by S´ark¨ozy. In subsequent papers, the minimum degree bound has been improved, most recently to (2/5 + ε)n by DeBiasio, Ferrara, and Morris. On the other hand no lower bounds close to this are known, and all papers on this topic ask whether the minimum degree needs to be linear. We answer this question, by showing that the required minimum degree for large Hamiltonian graphs to have a 2-factor consisting of a fixed number of cycles is sublinear in n.

Download activity - last month

Export as JSONCSVXML

Download activity - last 12 months

Export as JSONXMLCSV

Downloads by country - last 12 months

Export as JSONCSVXML

Archive Staff Only

View Item