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276
Codegree density of hypergraphs
 J. Combin. Theory (A
"... For an rgraph H, let C(H) = minS d(S), where the minimum is taken over all (r − 1)sets of vertices of H, and d(S) is the number of vertices v such that S ∪ {v} is an edge of H. Given a family F of rgraphs, the codegree Turán number coex(n,F) is the maximum of C(H) among all rgraphs H which c ..."
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Cited by 9 (3 self)
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For an rgraph H, let C(H) = minS d(S), where the minimum is taken over all (r − 1)sets of vertices of H, and d(S) is the number of vertices v such that S ∪ {v} is an edge of H. Given a family F of rgraphs, the codegree Turán number coex(n,F) is the maximum of C(H) among all rgraphs H which
Perfect Matchings and K 3 4Tilings in Hypergraphs of Large Codegree
"... For a kgraph F, let tl(n, m, F) be the smallest integer t such that every kgraph G on n vertices in which every lset of vertices is included in at least t edges contains a collection of vertexdisjoint Fsubgraphs covering all but at most m vertices of G. Let Kkm denote the complete kgraph on m ..."
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Cited by 3 (0 self)
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graph on m vertices. The function tk1(kn, 0, Kkk) (i.e. when we want to guarantee a perfect matching) has been previously determined by Kühn and Osthus [9] (asymptotically) and by Rödl, Ruci'nski, and Szemer'edi [13] (exactly). Here we obtain asymptotic formulae for some other l. Namely, we prove
Perfect Matchings and K³_4Tilings in Hypergraphs of Large Codegree
"... For a kgraph F, let tl(n, m, F) be the smallest integer t such that every kgraph G on n vertices in which every lset of vertices is included in at least t edges contains a collection of vertexdisjoint Fsubgraphs covering all but at most m vertices of G. Let Kkm denote the complete kgraph on ..."
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graph on m vertices. The function tk1(kn, 0, Kkk) (i.e. when we want to guarantee a perfect matching) has been previously determined by K"uhn and Osthus [6] (asymptotically) and by R"odl, Ruci'nski, and Szemer'edi [9] (exactly). Here we obtain the asymptotic formula for some
Treglown, Matchings in 3uniform hypergraphs
 J. Combin. Theory B
"... Abstract. Wedeterminetheminimumvertexdegreethatensuresaperfectmatchingina3uniform hypergraph. More precisely, supposethatH isasufficientlylarge 3uniform hypergraph whose order n is divisible by 3. If the minimum vertex degree of H is greater than ( ) () n−1 2n/3 − , then H contains a perfect matc ..."
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Cited by 7 (2 self)
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Abstract. Wedeterminetheminimumvertexdegreethatensuresaperfectmatchingina3uniform hypergraph. More precisely, supposethatH isasufficientlylarge 3uniform hypergraph whose order n is divisible by 3. If the minimum vertex degree of H is greater than ( ) () n−1 2n/3 − , then H contains a perfect
Tight codegree condition for perfect matchings in 4graphs, Electron
 J. Combin
"... We will give a tight minimum codegree condition for a 4uniform hypergraph to contain a perfect matching. 1 ..."
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Cited by 8 (0 self)
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We will give a tight minimum codegree condition for a 4uniform hypergraph to contain a perfect matching. 1
Minimum codegree threshold for hamilton cycles in kuniform hypergraphs
 Journal of Combinatorial Theory, Series A
, 2015
"... ar ..."
Extremal theory of codegree problems
, 2004
"... For an rgraph H, let C(H) = minS d(S), where the minimum is taken over all (r − 1)sets of vertices of H, and d(S) is the number of vertices v such that S ∪ {v} is an edge of H. Given a family F of rgraphs, the codegree Turán number coex(n, F) is the maximum of C(H) among all rgraphs H which c ..."
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For an rgraph H, let C(H) = minS d(S), where the minimum is taken over all (r − 1)sets of vertices of H, and d(S) is the number of vertices v such that S ∪ {v} is an edge of H. Given a family F of rgraphs, the codegree Turán number coex(n, F) is the maximum of C(H) among all rgraphs H which
Codegree problems for projective geometries
, 2007
"... The codegree density γ(F)of an rgraph F is the largest number γ such that there are Ffree rgraphs G on n vertices such that every set of r − 1 vertices is contained in at least (γ − o(1))n edges. When F = PG2(2) is the Fano plane Mubayi showed that γ(F) = 1/2. This paper studies γ(PGm(q)) for fur ..."
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Cited by 9 (4 self)
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The codegree density γ(F)of an rgraph F is the largest number γ such that there are Ffree rgraphs G on n vertices such that every set of r − 1 vertices is contained in at least (γ − o(1))n edges. When F = PG2(2) is the Fano plane Mubayi showed that γ(F) = 1/2. This paper studies γ
New bounds on nearly perfect matchings in hypergraphs: higher codegrees do help
 Random Struct. Alg
, 2000
"... Let H be a (k + 1)uniform, Dregular hypergraph on n vertices and U(H) be the minimum number of vertices left uncovered by a matching in H. Cj(H), the jcodegree of H, is the maximum number of edges sharing a set of j vertices in common. We prove a general upper bound on U(H), based on the codegr ..."
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Cited by 25 (5 self)
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Let H be a (k + 1)uniform, Dregular hypergraph on n vertices and U(H) be the minimum number of vertices left uncovered by a matching in H. Cj(H), the jcodegree of H, is the maximum number of edges sharing a set of j vertices in common. We prove a general upper bound on U(H), based
On the codegree threshold for the Fano plane
, 2014
"... Given a 3graph H, let ex2(n,H) denote the maximum value of the minimum codegree of a 3graph on n vertices which does not contain a copy of H. Let F denote the Fano plane, which is the 3graph {axx′, ayy′, azz′, xyz′, xy′z, x′yz, x′y′z′}. Mubayi [15] proved that ex2(n,F) = (1/2 + o(1))n and conjec ..."
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Given a 3graph H, let ex2(n,H) denote the maximum value of the minimum codegree of a 3graph on n vertices which does not contain a copy of H. Let F denote the Fano plane, which is the 3graph {axx′, ayy′, azz′, xyz′, xy′z, x′yz, x′y′z′}. Mubayi [15] proved that ex2(n,F) = (1/2 + o(1))n
Results 1  10
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276