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We show that every sufficiently large oriented graph G with Î´(G), Î´âˆ’(G) â‰¥

- Peter Keevash
- 2011

One of the earliest results in Combinatorics is Mantelâ€™s theorem from 1907 that the largest triangle-free graph on a given vertex set is complete bipartite. However, a seemingly similar questionâ€¦ (More)

Let F (n, r, k) denote the maximum possible number of distinct edge-colorings of a simple graph on n vertices with r colors, which contain no monochromatic copy of Kk. It is shown that for everyâ€¦ (More)

- Peter Keevash, Benny Sudakov
- Combinatorica
- 2005

Moreover, the only extremal configuration can be obtained by partitioning an n-element set into two almost equal parts, and taking all the triples that intersect both of them. This extends an earlierâ€¦ (More)

- Peter Keevash
- Random Struct. Algorithms
- 2011

We obtain a hypergraph generalisation of the graph blow-up lemma proved by KomlÃ³s, SarkÃ¶zy and SzemerÃ©di, showing that hypergraphs with sufficient regularity and no atypical vertices behave as ifâ€¦ (More)

- Peter Keevash, Fiachra Knox, Richard Mycroft
- STOC
- 2013

Let H be a k-graph on n vertices, with minimum codegree at least n/k + cn for some fixed c > 0. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in H or aâ€¦ (More)

- Tom Bohman, Peter Keevash
- 2009

The H-free process, for some fixed graph H, is the random graph process defined by starting with an empty graph on n vertices and then adding edges one at a time, chosen uniformly at random subjectâ€¦ (More)

- Peter Keevash, Dhruv Mubayi
- J. Comb. Theory, Ser. B
- 2004

A cancellative hypergraph has no three edges A;B;C with ADBCC: We give a new short proof of an old result of BollobÃ¡s, which states that the maximum size of a cancellative triple system is achievedâ€¦ (More)

- Peter Keevash, Daniela KÃ¼hn, Richard Mycroft, Deryk Osthus
- Discrete Mathematics
- 2011

We prove that any k-uniform hypergraph on n vertices with minimum degree at least n 2(kâˆ’1) + o(n) contains a loose Hamilton cycle. The proof strategy is similar to that used by KÃ¼hn and Osthus forâ€¦ (More)

- Peter Keevash
- Random Struct. Algorithms
- 2009

We describe a method that we believe may be foundational for a comprehensive theory of generalised TurÃ¡n problems. The cornerstone of our approach is a quasirandom counting lemma for quasirandomâ€¦ (More)