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Independent finite sums in graphs defined on the natural numbers

Tomasz Luczak, Vojtěch Rödl, Tomasz Schoen
1998 Discrete Mathematics  
In particular, we prove that if k, f >~ 2 and a graph G defined on the natural numbers contains no copies of the complete graph on k vertices, then there exists a subset A C ~ such that the set FS~ no  ...  An infinite version of this problem was stated by Andr~ts Hajnal, who asked if, for a graph G defined on the set of natural numbers, there exists an infinite set A with the above property.  ...  In particular, the set FS~<t(A) is independent.  ... 
doi:10.1016/s0012-365x(97)00064-2 fatcat:qh27gy4bjjaf5gzexnuflwot3m

Independence densities of hypergraphs

Anthony Bonato, Jason I. Brown, Dieter Mitsche, Paweł Prałat
2014 European journal of combinatorics (Print)  
In the case of finite but unbounded hyperedges, we show that the independence density can be any real number in [0, 1].  ...  We consider the number of independent sets in hypergraphs, which allows us to define the independence density of countable hypergraphs.  ...  The authors gratefully acknowledge support from NSERC, MPrime, and Ryerson University.  ... 
doi:10.1016/j.ejc.2014.03.001 fatcat:ecnbwhb75ne45mn3dke5icesxa

Independence densities of hypergraphs [article]

Anthony Bonato, Jason Brown, Dieter Mitsche, Pawel Pralat
2013 arXiv   pre-print
In the case of finite but unbounded hyperedges, we show that the independence density can be any real number in [0,1].  ...  We consider the number of independent sets in hypergraphs, which allows us to define the independence density of countable hypergraphs.  ...  We extend the definition of independence density of finite hypergraphs in the natural way to countable hypergraphs (which we define to be on a countable set of vertices but with edges of finite cardinality  ... 
arXiv:1308.2837v1 fatcat:cidyv45qejgwtbugpkrkn5id2e

On Factor Graphs and the Fourier Transform

Y. Mao, F.R. Kschischang
2005 IEEE Transactions on Information Theory  
We use these function extensions to derive a number of duality relationships among the corresponding factor graphs, and use these relationships to obtain the duality properties of Forney graphs as a special  ...  Convolutional and multiplicative factor graphs arise as natural Fourier transform duals.  ...  These comments have resulted in a substantially improved paper.  ... 
doi:10.1109/tit.2005.846404 fatcat:a3luxnr5frextpijbxullecqqm

Page 5939 of Mathematical Reviews Vol. , Issue 89K [page]

1989 Mathematical Reviews  
In the last section the exponential growth number of G is defined in the case when G is infinite and locally finite.  ...  It appears that this number is related to the essential isoperimetric number of G, defined by taking the supremum of the isoperimetric numbers of graphs ob- tained from G by adding or deleting finitely  ... 

The topology of graph products of groups

John Meier
1994 Proceedings of the Edinburgh Mathematical Society  
Given a finite (connected) simplicial graph with groups assigned to the vertices, the graph product of the vertex groups is the free product modulo the relation that adjacent groups commute.  ...  The graph product of finitely presented infinite groups is both semistable at infinity and quasi-simply filtrated.  ...  An isodiametric function for a presentation is a function I(n) from the natural numbers to the natural numbers, such that for the any set of words {co,} whose lengths sum to less than or equal to n, £i  ... 
doi:10.1017/s001309150001899x fatcat:dedq7im4n5eircdt5fapj7jkqe

Nilpotent adjacency matrices, random graphs and quantum random variables

René Schott, George Stacey Staples
2008 Journal of Physics A: Mathematical and Theoretical  
Each nilpotent adjacency matrix is a quantum random variable whose m th moment corresponds to the number of mcycles in the graph G.  ...  Using the generators of the subalgebra, an algebraic probability space of "nilpotent adjacency matrices" associated with finite graphs is defined.  ...  A graph is finite if V and E are finite sets, that is, if |V | and |E| are finite numbers. A loop in a graph is an edge of the form (v, v).  ... 
doi:10.1088/1751-8113/41/15/155205 fatcat:pbt56hdivfeavnz77fs6vhu5am

Page 3591 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
A hypergraph has property (S) if every minimal transversal is the support of a stochastic function. Sums and products of hypergraphs are defined in a natural way.  ...  the number of edges in the graph.”  ... 

Hodge Theory of Matroids

Karim Adiprasito, June Huh, Eric Katz
2017 Notices of the American Mathematical Society  
If is the set of edges of a finite graph , call a subset of a flat when there is no edge in \ whose endpoints are connected by a path in . This defines a graphic matroid on .  ...  Write for a finite subset of a vector space and ( ) for the number of independent subsets of of size . Example 3.  ... 
doi:10.1090/noti1463 fatcat:qe5ouzu5cbbgbp3zov6mk4a734

Author index to volume 181 (1998)

1998 Discrete Mathematics  
Schoen, Independent finite sums in graphs defined on the natural numbers (Note) , A.N., On k-weak orders: Recognition and a tolerance result (1-3) Tsai, Y.S., see H.J. Shyr (1-3)  ...  Ordaz, Neighborhood conditions for balanced independent sets in bipartite graphs (1 3 B6na, M., Permutations with one or two 132-subsequences (Note) (1 3 Bogart, K.P. and G.  ... 
doi:10.1016/s0012-365x(97)82062-6 fatcat:sqdp43rjovam5az5gxnwxknhxq

Page 1344 of Mathematical Reviews Vol. , Issue 85d [page]

1985 Mathematical Reviews  
The Ramsey number r(m,n) is defined to be the smallest integer p such that every graph of order p contains either a complete subgraph on m vertices or a set of n independent vertices.  ...  In previous papers the author has shown that many of the spectral properties for finite graphs carry over to the newly defined infinite case [Publ. Inst. Math.  ... 

On the density of sets of the Euclidean plane avoiding distance 1 [article]

Thomas Bellitto, Arnaud Pêcher, Antoine Sédillot
2021 arXiv   pre-print
In this paper we study the number m_1(ℝ^2) which is the supremum of the upper densities of measurable sets avoiding distance 1 in the Euclidean plane.  ...  This parameter is related to the fractional chromatic number χ_f(ℝ^2) of the plane. We establish that m_1(ℝ^2) ≤ 0.25647 and χ_f(ℝ^2) ≥ 3.8991.  ...  The fractional chromatic number of a graph G (finite or not), χ f (G), is then defined as χ f (G) = inf b χ b (G) b .  ... 
arXiv:1810.00960v3 fatcat:4tt224lztvbz7epak3jpfgcqfq

Finite-Time and Fixed-Time Consensus of Multiagent Networks with Pinning Control and Noise Perturbation

Yongzheng Sun, Wang Li, Hongjun Shi, Donghua Zhao, Sandro Azaele
2019 SIAM Journal on Applied Mathematics  
Unlike the finite-time control, the settling time of network systems with fixed-time control is independent of the  ...  Our analysis will naturally lead to looking into how the settling time of the finitetime consensus depends on the initial states of the system.  ...  Let i \in \scrV ; then the graph p-Laplacian is defined as (3.1) (\Delta p \zeta ) i = \sum j\in \scrN i a ij \phi p (\zeta i -\zeta j ), where \zeta is a function on \scrV and \phi p : \BbbR \rightar  ... 
doi:10.1137/18m1174143 fatcat:hzarp2t2qrhl3dxmb7cpsubprq

Politopos en filogenética

Linard Hoessly
2021 Tequio  
to natural numbers.  ...  The Tight span and the Lipschitz polytope are both associated to finite metric spaces and can be connected to distance-preserving embeddings, while the balanced minimum evolution (BME) polytope is associated  ...  The minimum evolution polytope on the other hand is associated to natural numbers ∈ ℕ nA . In the following, we aim to introduce and motivate the main objects.  ... 
doi:10.53331/teq.v4i11.0649 fatcat:gwl32d6xzjdhzn54u7vxho566a

Entropy and expansion [article]

Endre Csóka, Viktor Harangi, Bálint Virág
2020 arXiv   pre-print
The proof method yields inequalities for other measures of randomness, including covariance. As an application, we give upper bounds for independent sets in both finite and infinite graphs.  ...  We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of independent random seeds.  ...  Bálint Virág was also supported by the Canada Research Chair program, the NSERC Discovery Accelerator grant, and the ERC Consolidator Grant InvGroGra 648017.  ... 
arXiv:1811.09560v3 fatcat:2oshadkqp5ghvg7k5davqccj4a
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