Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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

Mittagsseminar Talk Information

Date and Time: Tuesday, May 14, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Matija Bucic

Covering random graphs by monochromatic trees and Helly-type results for hypergraphs

How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given r-edge-coloured graph G? These problems were introduced in the 1960's and were intensively studied by various researchers over the last 50 years. We consider the question of covering random graphs using monochromatic trees, introduced by Bal and DeBiasio. Surprisingly, it is closely connected to the following, independently interesting, Helly-type problem about vertex covers of hypergraphs. Roughly speaking, the question is how large a cover of a hypergraph H can be if any subgraph of H with few edges has a small cover. We prove good bounds for the hypergraph problem and use them to estimate quite accurately the number of monochromatic trees needed to cover a random graph. Our results provide some very surprising answers to several questions in the area asked by Bal and DeBiasio, Kohayakawa, Mota and Schacht, Lang and Lo and Girao, Letzter and Sahasrabudhe. This is joint work with D. Korandi and B. Sudakov.

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