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

Date and Time: Thursday, March 13, 2025, 12:15 pm

Duration: 30 minutes

Location: CAB G52

Speaker: Matija Pasch

Improved Universal Graphs for Trees

A graph G=(V,E) is universal for a class of graphs if G contains each graph in the class as a subgraph (up to isomorphism). We focus on the special case where G is tree-complete, that is, G contains each tree on |V| vertices as a subgraph. In 1978, Chung and Graham asked for the minimal number s(n) of edges of a tree-complete graph on n vertices. The currently best known lower bound (up to lower order terms) for s(n) is n ln(n) and the best known upper bound is Cn ln(n), where C is approximately 3.606. We improve the upper bound to cn ln(n), where c is approximately 2.882. To establish this result, we develop a strategy that, broadly speaking, is based on separating trees into three parts. This enables us to embed the trees in a structure that originates from ternary trees. We further show that our strategy is optimal in a certain sense. This talk is based on joint work with Julian Becker and Konstantinos Panagiotou.

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

Previous talks by year:   2025  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