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Limits of dense graph sequences
 J. Combin. Theory Ser. B
"... We show that if a sequence of dense graphs Gn has the property that for every fixed graph F, the density of copies of F in Gn tends to a limit, then there is a natural “limit object”, namely a symmetric measurable function W: [0,1] 2 → [0, 1]. This limit object determines all the limits of subgraph ..."
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Cited by 207 (18 self)
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We show that if a sequence of dense graphs Gn has the property that for every fixed graph F, the density of copies of F in Gn tends to a limit, then there is a natural “limit object”, namely a symmetric measurable function W: [0,1] 2 → [0, 1]. This limit object determines all the limits of subgraph
Decompositions of triangledense graphs
 In 5th Conference on Innovations in Theoretical Computer Science (ITCS
, 2014
"... High triangle density — the graph property stating that a constant fraction of twohop paths belong to a triangle — is a common signature of social networks. This paper studies triangledense graphs from a structural perspective. We prove constructively that significant portions of a triangledense ..."
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Cited by 6 (3 self)
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High triangle density — the graph property stating that a constant fraction of twohop paths belong to a triangle — is a common signature of social networks. This paper studies triangledense graphs from a structural perspective. We prove constructively that significant portions of a triangledense
Hfactors in dense graphs
 Graphs and Combinatorics 8
, 1996
"... The following asymptotic result is proved. For every fixed graph H with h vertices, any graph G with n vertices and with minimum degree d ≥ χ(H)−1 χ(H) n contains (1 − o(1))n/h vertex disjoint copies of H. ..."
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Cited by 73 (6 self)
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The following asymptotic result is proved. For every fixed graph H with h vertices, any graph G with n vertices and with minimum degree d ≥ χ(H)−1 χ(H) n contains (1 − o(1))n/h vertex disjoint copies of H.
Percolation on Dense Graph Sequences
, 2007
"... In this paper, we determine the percolation threshold for an arbitrary sequence of dense graphs (Gn). Let λn be the largest eigenvalue of the adjacency matrix of Gn, and let Gn(pn) be the random subgraph of Gn that is obtained by keeping each edge independently with probability pn. We show that the ..."
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Cited by 10 (4 self)
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In this paper, we determine the percolation threshold for an arbitrary sequence of dense graphs (Gn). Let λn be the largest eigenvalue of the adjacency matrix of Gn, and let Gn(pn) be the random subgraph of Gn that is obtained by keeping each edge independently with probability pn. We show
ON NOWHERE DENSE GRAPHS
"... A set A of vertices of a graph G is called dscattered in G if no two dneighborhoods of (distinct) vertices of A intersect. In other words, A is dscattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and rec ..."
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Cited by 7 (0 self)
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of nowhere dense graphs are quasi wide. This not only strictly generalizes the previous results and solves several open problems but it also provides new proofs. It appears that bounded expansion and nowhere dense classes are perhaps a proper setting for investigation of widetype classes as in several
On Nowhere Dense Graphs
"... A set A of vertices of a graph G is called dscattered in G if no two dneighborhoods of (distinct) vertices of A intersect. In other words, A is dscattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and rece ..."
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Cited by 3 (0 self)
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of nowhere dense graphs are quasi wide. This not only strictly generalizes the previous results and solves several open problems but it also provides new proofs. It appears that bounded expansion and nowhere dense classes are perhaps a proper setting for investigation of widetype classes as in several
2factors in dense graphs
 Discrete Math
, 1996
"... A conjecture of Sauer and Spencer states that any graph G on n vertices with minimum degree at least 2 3n contains any graph H on n vertices with maximum degree 2 or less. This conjecture is proven here for all sufficiently large n. 1 ..."
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Cited by 7 (0 self)
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A conjecture of Sauer and Spencer states that any graph G on n vertices with minimum degree at least 2 3n contains any graph H on n vertices with maximum degree 2 or less. This conjecture is proven here for all sufficiently large n. 1
Spanning Trees in Dense Graphs
, 2001
"... In this paper we prove the following almost optimal theorem. For any δ>0, there exist constants c and n0 such that, if n � n0, T is a tree of order n and maximum degree at most cn / log n, and G is a graph of order n and minimum degree at least (1/2+δ)n, then T is a subgraph of G. ..."
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Cited by 8 (0 self)
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In this paper we prove the following almost optimal theorem. For any δ>0, there exist constants c and n0 such that, if n � n0, T is a tree of order n and maximum degree at most cn / log n, and G is a graph of order n and minimum degree at least (1/2+δ)n, then T is a subgraph of G.
Adding Random Edges to Dense Graphs
 Random Structures Algorithms
, 2003
"... This paper investigates the addition of random edges to arbitrary dense graphs; in particular, we determine the number of random edges required to ensure various monotone properties including the appearance of a xed size clique, diameter and kconnectivity. ..."
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Cited by 3 (1 self)
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This paper investigates the addition of random edges to arbitrary dense graphs; in particular, we determine the number of random edges required to ensure various monotone properties including the appearance of a xed size clique, diameter and kconnectivity.
Results 1  10
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