Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, July 05, 2016, 12:15 pm

Duration: 30 minutes

Location: CAB G11

Speaker: Miloš Trujić

An extension of Dirac's theorem for sparse graphs (Master Thesis)

The celebrated result of Dirac states that any graph on n > 2 vertices with minimum degree at least n/2 contains a Hamilton cycle. Recently, Balogh, Mousset, and Skokan generalised this result by showing that for any integer k > 1 and sufficiently large n, the vertex set of a graph G on n vertices with minimum degree at least n/k can be covered by at most k - 1 cycles.

In this thesis we extend the result of Balogh et al. to a sparse setting. Namely, we show that for any integer k > 1 the vertex set of a random graph G(n, p) with p > n^(-1 + o(1)) can be covered by at most k - 1 cycles even after removing at most ((k - 1)/k - o(1))-fraction of the edges touching each vertex. Our results are optimal with respect to the constant (k - 1)/k and almost optimal with respect to the edge probability p.

Thesis supervised by Angelika Steger, Frank Mousset, and Nemanja Škorić.

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

Previous talks by year:   2024  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