Counting Graph Homomorphisms

By Christian Borgs, Jennifer Tour Chayes, L. Lov'asz, Vera T. Sós, Katalin Vesztergombi. 2006

213 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c282d7cfc6faa93c142c84c8be0c6fec8c5ddeb4

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

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Citations in the corpus

Moments of Two-Variable Functions and the Uniqueness of Graph Limits (2008, background): “limit for every simple graph F. The notion of convergent graph sequences was introduced by Borgs, Chayes, Lov¶asz, S¶os and Vesztergombi [2], see also [ 3 ], and further studied in [4] and [5].”
An $L^{p}$ theory of sparse graph convergence II: LD convergence, quotients and right convergence (2014, background): “where the infimum is over all invertible maps φ : [0,1] → [0,1] such that both φ and its inverse are measure preserving, and W is defined by W(x, y) = W(φ(x),φ(y)) (see [7, 8, 12]); such a map φ is called a measure-preserving bijection.”
Metrics for sparse graphs (2007, background): “Borgs, Chayes, Lovász, Sós and Vesztergombi [15, 16] consider weighted graphs, with weights on the edges and on the vertices.”
The number of cliques in graphs of given order and size (2007, background): “Most recently, the problem was discussed in detail in [1] and [9].”
Random graphs with a given degree sequence (2010, background): “By Sourav Chatterjee1, Persi Diaconis and Allan Sly”
Percolation on dense graph sequences. (2007, methodology): “Borgs, Chayes, Lovász, Sós and Vesztergombi in [12] (see also [13]).”
An introduction to large deviations for random graphs (2016, background): “graphs [5, 42]. This theory is discussed in Sections 7 through 10. 4. Graph limit theory A beautiful unifying theory of graph limits has been developed by Laszlo Lov´asz and coauthors in recent years [8, 9, 10, 40, 41]. For connections with the theory of exchangeable arrays in probability theory, se”
Matrix estimation by Universal Singular Value Thresholding (2012, background): “The term ‘graphon’ was coined by Lov´asz and coauthors in the growing literature on limits of dense graphs [19, 20, 21, 69, 68].”
Convergent Sequences of Dense Graphs II. Multiway Cuts and Statistical Physics (2012, background): “This paper is the second of two papers in which we develop a theory of convergent sequences of dense graphs; see [5] for an announcement of some of these results.”
Convergent Sequences of Dense Graphs I: Subgraph Frequencies, Metric Properties and Testing (2007, background): “7, which is still strong enough to prove the equivalence of leftconvergence and convergence in metric (see [16] for details).”
Asymptotic behavior and distributional limits of preferential attachment graphs (2014, methodology): “Indeed, for sequences of graphs Gn whose degree is bounded uniformly in n, this notion can easily be shown to be equivalent to the notion introduced by Benjamini and Schramm; moreover, the corresponding notions involving the number of injective homomorphisms, or the number of induced subgraphs, are ”