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

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, December 02, 2014, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Frank Mousset

## Packing a randomly edge-colored random graph with rainbow k-outs

Let G be a graph on n vertices and let k,c be fixed positive integers. The random subgraph G_k of G is obtained by letting each vertex of G pick k neighbours uniformly at random from its neighbourhood in G ("k-out"). The edge-coloured random subgraph G(p,c) of G is obtained by keeping each edge independently with probability p, and then colouring each edge randomly with a color from the set {1,...,c}.

We show that if p >> log n/delta(G), then in a typical H ~ G(p,kn), one can find t = (1-o(1)) delta(G)p/(2k) edge-disjoint subgraphs H_i, with the following properties: (a) each H_i is almost distributed like G_k, in the sense that monotone properties of G_k transfer to H_i; (b) each H_i is rainbow, i.e., each edge is painted in a different colour. Since the typical vertex of G_k has degree 2k, and since the minimum degree of G(p,kn) is delta(G)p, this result is asymptotically optimal. Let G be a graph on n vertices and let k,c be fixed positive integers. The random subgraph G_k of G is obtained by letting each vertex of G pick k neighbours uniformly at random from its neighbourhood in G ("k-out"). On the other hand, the edge-coloured random subgraph G(p,c) is obtained by keeping each edge independently with probability p, and then colouring each edge randomly with a color from the set {1,...,c}.

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