Fractional decompositions of dense graphs

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• Richard Montgomery (University of Cambridge)
• Thursday 09 November 2017, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

It is difficult to determine when a graph G can be edge-covered by edge-disjoint copies of a fixed graph F. That is, when it has an F-decomposition. However, subject to some simple divisibility conditions, a high minimum degree is known to force such a decomposition in large graphs. Recent research has strongly linked reducing the degree bound required here to comparable results for a relaxation of this problem, where a fractional decomposition is sought.

I will show how a relatively simple random process can give a good starting approximation to a fractional decomposition, and how it subsequently can be corrected. This improves the best known bounds until the permitted discrepancy in degree is within a constant factor of the conjectured maximum.

This talk is part of the Combinatorics Seminar series.

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