University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Dirac-type results for tilings and coverings in ordered graphs

Dirac-type results for tilings and coverings in ordered graphs

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If you have a question about this talk, please contact Eoin Long.

A (vertex) ordered graph H on h vertices is a graph whose vertices have been labelled with {1, . . . , h}. Balogh, Li and Treglown recently initiated the study of Dirac-type problems for ordered graphs. In particular, they focused on the problem of determining the minimum degree threshold for forcing a perfect H-tiling in an ordered graph for any fixed ordered graph H (recall that a perfect H-tiling in a graph G is a collection of vertex-disjoint copies of H covering all the vertices in G). In this talk we present a result which builds up on their ideas and fully resolve such problem. We also determine the asymptotic minimum degree threshold for forcing an H-cover in an ordered graph. This is joint work with Andrew Treglown.

This talk is part of the Combinatorics and Probability seminar series.

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