Journal ArticleDOI
On the Local Approach to Sidorenko's Conjecture
Jacob Fox,Fan Wei +1 more
TLDR
A local version of the forcing conjecture holds locally for H if and only if H has even girth or is a forest, and it is proved that for such H there is δ H > 0 such that Sidorenko's conjecture and theforcing conjecture holds for all p > 1 −δ H .About:
This article is published in Electronic Notes in Discrete Mathematics.The article was published on 2017-08-01. It has received 15 citations till now. The article focuses on the topics: Lonely runner conjecture & Collatz conjecture.read more
Citations
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Cut distance identifying graphon parameters over weak* limits
TL;DR: In this article, the authors studied graphon parameters with the property that their minimizers or maximizers identify cut distance accumulation points over the set of weak* accumulation points, called cut distance identifying.
Journal ArticleDOI
The step Sidorenko property and non-norming edge-transitive graphs
TL;DR: It is shown that many bipartite graphs fail to have the step Sidorenko property and the results are used to show the existence of a bipartites edge-transitive graph that is not weakly norming; this answers a question of Hatami.
Journal ArticleDOI
Supersaturation of C4: From Zarankiewicz towards Erdős–Simonovits–Sidorenko
TL;DR: In this article, it was shown that for a positive integer n, a graph F and a bipartite graph G ⊆ K n, n, if m and the corresponding Zarankiewicz number differ by c ⋅ n n, then F = K 2, t and in particular the quadrilateral graph case, it is possible to obtain exact results for F = C 4 by a finite geometric construction of almost difference sets.
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Non-bipartite k-common graphs
TL;DR: A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring as discussed by the authors.
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Unified approach to the generalized Tur\'an problem and supersaturation
TL;DR: The supersaturation-extremal function is defined in this article as the least number of copies of a subgraph that an n-vertex graph can have, which contains at least $m$ copies of the subgraph as a sub-graph.
References
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Book
Large Networks and Graph Limits
TL;DR: Laszlo Lovasz has written an admirable treatise on the exciting new theory of graph limits and graph homomorphisms, an area of great importance in the study of large networks.
Journal ArticleDOI
On the structure of linear graphs
Paul Erdös,A. H. Stone +1 more
TL;DR: The first result in this direction was due to Turân as discussed by the authors, who proved that a graph with kn vertices and Ck, 2n+1 edges always contains a complete graph of order k + 1.
Journal ArticleDOI
Convergent sequences of dense graphs I: Subgraph frequencies, metric properties and testing
TL;DR: In Part I of this series, we showed that left convergence is equivalent to convergence in metric, both for simple graphs and for graphs with nodeweights and edgeweights as discussed by the authors.
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On the minimal density of triangles in graphs
TL;DR: This paper proves that g_3(\rho) is the minimal possible density of triangles in a graph with edge density ρ by proving that $t\df \lfloor 1/(1-\rho)\rfloor$ is the integer such that $\rho\in\bigl[ 1-\frac 1t,1- \frac 1{t+1}\bigr]$.