Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, May 16, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Erik Jahn

2-factors with k cycles in Hamiltonian graphs

A theorem by Brandt, Chen, Gould, Faudree and Lesniak 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 quickly 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 Sarközy and after a series of improvements the best known result, due to DeBiasio, Ferrara and Morris, established that a minimum degree of (2/5 + o(1))n suffices. We present a major improvement of this result 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. This is joint work with M. Bucic, A. Pokrovskiy and B. Sudakov.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login