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Osthus, Deryk


Graph Theory » Hypergraphs

Simultaneous partition of hypergraphs ★★

Author(s): Kühn; Osthus

Problem   Let $ H_1 $ and $ H_2 $ be two $ r $-uniform hypergraph on the same vertex set $ V $. Does there always exist a partition of $ V $ into $ r $ classes $ V_1, \dots , V_r $ such that for both $ i=1,2 $, at least $ r!m_i/r^r -o(m_i) $ hyperedges of $ H_i $ meet each of the classes $ V_1, \dots , V_r $?

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Posted by fhavet
updated March 6th, 2013
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Graph Theory » Extremal G.T.

Complexity of the H-factor problem. ★★

Author(s): Kühn; Osthus

An $ H $-factor in a graph $ G $ is a set of vertex-disjoint copies of $ H $ covering all vertices of $ G $.

Problem  Let $ c $ be a fixed positive real number and $ H $ a fixed graph. Is it NP-hard to determine whether a graph $ G $ on $ n $ vertices and minimum degree $ cn $ contains and $ H $-factor?

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Posted by fhavet
updated March 5th, 2013
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