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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, September 24, 2015, 12:15 pm

**Duration**: 30 minutes

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

**Speaker**: Frank Mousset

A sequence G_{1},...,G_{t} of graphs is said to *pack* into a graph G if G contains G_{1},...,G_{t} as edge-disjoint subgraphs. I will talk about the following result. Let F be a non-trivial minor-closed family of graphs (for example, the family of planar graphs). Then for all positive constants x and D and for every sufficiently large integer n, every sequence G_{1},...,G_{t} of graphs in F such that

- v(G_{i}) ≤ n for all i,

- e(G_{1}) + ... + e(G_{t}) ≤ (1-x) n(n-1)/2, and

- the maximum degree of each G_{i} is at most D,

packs into the complete graph on n vertices. This improves a very similar result of Messuti, Rödl, and Schacht in which the graphs are required to have at most (1-x)n vertices.

Joint work with Asaf Ferber and Choongbum Lee.

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