Andrew Treglown (Queen Mary, University of London): On generalisations of the Hajnal-Szemerédi theorem |
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Péntek, 11. Április 2014, 10:30 - 12:00
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| Abstract. We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. The seminal Hajnal-Szemerédi theorem states that every graph G whose order n is divisible by r and whose minimum degree is at least (1-1/r)n contains a perfect K_r-packing. It is easy to see that the minimum degree condition here is "best-possible". Balogh, Kostochka and the speaker gave a conjecture on the degree sequence of a graph G that forces a perfect K_r-packing in G. If true, the conjecture is a strong generalisation of the Hajnal-Szemerédi theorem as it allows for n/r vertices in G to have degree less than (1-1/r)n. In this talk I will mention a very recent asymptotic solution to this conjecture. I will also discuss recent results on generalising the Hajnal-Szemerédi theorem to the directed graph setting. |
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Hely : Kalmár Intézet, Árpád tér, szemináriumi szoba |
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