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Intersections of graphs
, 2010
"... Let G and H be two graphs of order n. If we place copies of G and H on a common vertex set, how much or little can they be made to overlap? The aim of this paper is to provide some answers to this question, and to pose a number of related problems. Along the way, we solve a conjecture of Erdős, Gold ..."
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Cited by 6 (2 self)
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Let G and H be two graphs of order n. If we place copies of G and H on a common vertex set, how much or little can they be made to overlap? The aim of this paper is to provide some answers to this question, and to pose a number of related problems. Along the way, we solve a conjecture of Erdős, Goldberg, Pach and Spencer. 1
Making a K4free graph bipartite
 COMBINATORICA
, 2007
"... We show that every K4free graph G with n vertices can be made bipartite by deleting at most n²/9 edges. Moreover, the only extremal graph which requires deletion of that many edges is a complete 3partite graph with parts of size n/3. This proves an old conjecture of P. Erdős. ..."
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Cited by 1 (1 self)
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We show that every K4free graph G with n vertices can be made bipartite by deleting at most n²/9 edges. Moreover, the only extremal graph which requires deletion of that many edges is a complete 3partite graph with parts of size n/3. This proves an old conjecture of P. Erdős.
Intersections of hypergraphs
, 2012
"... Given two weighted kuniform hypergraphs G, H of order n, how much (or little) can we make them overlap by placing them on the same vertex set? If we place them at random, how concentrated is the distribution of the intersection? The aim of this paper is to investigate these questions. 1 ..."
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Cited by 1 (1 self)
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Given two weighted kuniform hypergraphs G, H of order n, how much (or little) can we make them overlap by placing them on the same vertex set? If we place them at random, how concentrated is the distribution of the intersection? The aim of this paper is to investigate these questions. 1
Note Sparse halves in trianglefree graphs
, 2006
"... One of Erdős’ favourite conjectures was that any trianglefree graph G on n vertices should contain a set of n/2 vertices that spans at most n²/50 edges. We prove this when the number of edges in G is either at most n²/12 or at least n²/5. ..."
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One of Erdős’ favourite conjectures was that any trianglefree graph G on n vertices should contain a set of n/2 vertices that spans at most n²/50 edges. We prove this when the number of edges in G is either at most n²/12 or at least n²/5.