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

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, November 03, 2020, 12:15 pm

**Duration**: 30 minutes

**Location**: Zoom: conference room

**Speaker**: Nemanja Draganic

## Rolling backwards can move you forward: on embedding problems in sparse expanders

We develop a general embedding method based on the Friedman-Pippenger tree embedding technique (1987) and its algorithmic version, enhanced with a roll-back idea allowing to sequentially retrace previously performed embedding steps. This proves to be a powerful tool for embedding graphs of large girth into expander graphs. As an application of this method, we settle two problems:

-For a graph $H$, we denote by $H^q$ the graph obtained from $H$ by subdividing its edges with $q-1$ vertices each. We show that the $k$-size-Ramsey number $\hat{R}_k(H^q)$ satisfies $\hat{R}_k(H^q)=O(qn)$ for every bounded degree graph $H$ on $n$ vertices and for $q=\Omega(\log n)$, which is optimal up to a constant factor. This settles a conjecture of Pak (2002).

-We give a deterministic, polynomial time algorithm for finding vertex-disjoint paths between a given number of pairs of vertices (which is optimal up to a constant factor) in a strong expander graph. The result answers the offline version of a question of Alon and Capalbo (2007).

Joint work with Michael Krivelevich And Rajko Nenadov.

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