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Page 6760 of Mathematical Reviews Vol. , Issue 98K [page]

1998 Mathematical Reviews  
A tree of type (k,/,m,n, p), where ged(k,/,m,n, p) = 1, is generic. A. A. Makhnev (Yekaterinburg) 98k:05048 05C05 Polat, Norbert (F-LYON3-IA; Lyon) End-faithful spanning trees in 7. -free graphs.  ...  Summary: “We prove that any connected graph that contains no subdivision of an &j-regular tree has an end-faithful spanning tree, and furthermore that it has a rayless spanning tree if all its ends are  ... 

Systematic Correct Construction of Self-stabilizing Systems: A Case Study [chapter]

Ananda Basu, Borzoo Bonakdarpour, Marius Bozga, Joseph Sifakis
2010 Lecture Notes in Computer Science  
This model is used for performance analysis taking into account the degree of parallelism and convergence times for failure-free behavior as well as in the presence of faults.  ...  First, a high-level model of the algorithm is built in BIP from the set of its processes by using powerful primitives for multi-party interactions and scheduling.  ...  The graphs clearly show that crash faults' damage to the spanning tree is more severe than the case where a process has wrong coordinates of the root.  ... 
doi:10.1007/978-3-642-16023-3_4 fatcat:scrqkkfterbe7bpbpe7mrvyrmq

Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs

Dieter Kratsch, Ross M. McConnell, Kurt Mehlhorn, Jeremy P. Spinrad
2006 SIAM journal on computing (Print)  
We give linear-time certifying algorithms for recognition of interval graphs and permutation graphs.  ...  We show that our certificates of non-membership can be authenticated in O(IV[) time.  ...  A spanning tree in F U does not have size that is linear in the size of G.  ... 
doi:10.1137/s0097539703437855 fatcat:3n6avwreznbdbks6aixloyldga

Graphs and complexes of lattices [article]

Sam Hughes
2022 arXiv   pre-print
To do this we introduce the notions of a graph of lattices and a complex of lattices giving graph and complex of group splittings of CAT(0) lattices.  ...  Using this framework we characterise irreducible uniform (Isom(𝔼^n)× T)-lattices by C^∗-simplicity and give a necessary condition for lattices in products with a Euclidean factor to be biautomatic.  ...  Secondly, with respect to a maximal or spanning tree of the graph.  ... 
arXiv:2104.13728v4 fatcat:57y7m47urbeo5gca5qjgdyajue

The petit topos of globular sets

Ross Street
2000 Journal of Pure and Applied Algebra  
For example, higher spans turn out to be internal sets, and, in a sense, trees turn out to be internal natural numbers. c 2000 Elsevier Science B.V. All rights reserved.  ...  -categories A globular set is an inÿnite-dimensional graph.  ...  So Tree is the free !-category 1 on the terminal globular set 1. It is shown in [2] that 1 is the !-category of higher trees.  ... 
doi:10.1016/s0022-4049(99)00183-8 fatcat:ckpvabdpvzdj5fb2zpl6c35hoa

The Component Graph of the Uniform Spanning Forest: Transitions in Dimensions 9,10,11,.. [article]

Tom Hutchcroft, Yuval Peres
2018 arXiv   pre-print
In particular, we consider the graph formed by contracting each tree of the uniform spanning forest down to a single vertex, which we call the component graph.  ...  We prove that the uniform spanning forests of Z^d and Z^ℓ have qualitatively different connectivity properties whenever ℓ >d ≥ 4.  ...  and the ith pair of trees all intersect some ball Bi of radius r in G for each i = 1, 2, 3, and the trees T1 , T2 , T3 all intersect some ball B0 of radius r in G.  ... 
arXiv:1702.05780v2 fatcat:tm7xikskl5eglixh3slhdzihhe

Context-Free Groups and Bass-Serre Theory [article]

Volker Diekert, Armin Weiß
2017 arXiv   pre-print
In a seminal paper Muller and Schupp showed the converse: A context-free group is virtually free. Over the past decades a wide range of other characterizations of context-free groups have been found.  ...  The word problem of a finitely generated group is the formal language of words over the generators which are equal to the identity in the group.  ...  Lemma 1.6 Every connected undirected graph has a spanning tree. Remark 1.7 In fact, an easy exercise shows that the existence of a spanning tree is equivalent to the axiom of choice.  ... 
arXiv:1307.8297v2 fatcat:lmhksz677baapcmn7mn6qcohma

Geometry and combinatorics via right-angled Artin groups [article]

Thomas Koberda
2021 arXiv   pre-print
The final version of this survey will appear in "In the tradition of Thurston, vol.~II", ed.~K.~Ohshika and A.~Papadopoulos.  ...  We concentrate on the defining graph of the right-angled Artin group and on the extension graph associated to the right-angled Artin group.  ...  Now, if K Ă t1, . . . , nu consists of a collection of vertices which span a complete subgraph of Γ, then we include the subcube of r0, 1s n spanned by tJ i u iPK in S .  ... 
arXiv:2103.09342v2 fatcat:e5wct6yanbeorhulyrcksvej4a

General Operads and Multicategories [article]

Tom Leinster
1998 arXiv   pre-print
This work provides a single framework in which many of these various notions can be expressed.  ...  It was prepared in L A T E X using Paul Taylor's commutative diagrams package. My thanks go to Martin Hyland for encouraging me to pursue this line of enquiry.  ...  The unit X E X * is x −→ x •, and multiplication X * * E X * takes an X * -labelled tree (e.g. • t1 • • • t2 • • , with t 1 = x2 • x1 • • • and t 2 = • x3 • • x4 • • • ) and gives an X-labelled tree by  ... 
arXiv:math/9810053v1 fatcat:lbjcyxwtjrf6pdk6lmzgdtwfhe

Traffic distributions and independence: permutation invariant random matrices and the three notions of independence [article]

Camille Male
2018 arXiv   pre-print
A central limiting theorem is stated in this context, interpolating between the tensor, free and Boolean central limit theorems.  ...  We prove that at an algebraic level, traffic independence in some sense unifies the three canonical notions of tensor, free and Boolean independence.  ...  The author thanks Antoine Dahlqvist and Guillaume Cébron for their help in correcting an error in Proposition 3.7, Benson Au for his careful proofreading, and the reviewers for their suggestions.  ... 
arXiv:1111.4662v8 fatcat:akvbfvezgne4hasjmtq5n6zo7u

Regular completions of ℤ^n-free groups [article]

Olga Kharlampovich, Alexei Miasnikov, Denis Serbin
2021 arXiv   pre-print
In the present paper we continue studying regular free group actions on ℤ^n-trees.  ...  We show that every finitely generated ℤ^n-free group G can be embedded into a finitely generated ℤ^n-free group H acting regularly on the underlying ℤ^n-tree (we call H a regular ℤ^n-completion of G) so  ...  Serbin showed that groups admitting faithful representations by Λ-words act freely on Λ-trees, while Chiswell proved the converse [6] .  ... 
arXiv:1208.4640v2 fatcat:bkpib3ejhrdb7nmutp5qhxsjsa

Tree Topology Estimation

Rolando Estrada, Carlo Tomasi, Scott C. Schmidler, Sina Farsiu
2015 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Tree Topology Estimation Abstract Tree-like structures are fundamental in nature. A wide variety of two-dimensional imaging techniques allow us to image trees.  ...  We regularize this inverse problem via a prior parametric tree-growth model that realistically captures the morphology of a wide variety of trees.  ...  Connect these edges to the spanning tree at either end-arbitrarily or according to a topological sorting-and orient them consistently away from r G . The resulting graph is a G-tree.  ... 
doi:10.1109/tpami.2014.2382116 pmid:26353004 pmcid:PMC4566856 fatcat:7tlcg7zegjdlrngwsodn6zjc6q

Operads in Higher-Dimensional Category Theory [article]

Tom Leinster
2000 arXiv   pre-print
expounded by Baez, Dolan and others, and are a natural language in which to discuss enrichment of categorical structures.  ...  The purpose of this dissertation is to set up a theory of generalized operads and multicategories, and to use it as a language in which to propose a definition of weak n-category.  ...  The document was prepared in L A T E X, using Paul Taylor's diagrams package for some of the diagrams. Audrey Tan helped me prettify it.  ... 
arXiv:math/0011106v1 fatcat:k6ajmcd6u5dqjefj4zohtpz45u

An operad of non-commutative independences defined by trees

David Jekel, Weihua Liu
2020 Dissertationes Mathematicae  
If T ∈ Tree(k) and T ∈ Tree(n j ) for j = 1, . . . , k, then T ( T1 , . . . , T k ) = T (T1,...,T k ) . In other words, T → T is an operad morphism. Proof.  ...  strings on {1, 2} that end in 12.  ...  T ( T1 , . . . , T k ) = T (T1,...,T k ) .  ... 
doi:10.4064/dm797-6-2020 fatcat:pmturbkiljev5d3bvuodrrxuqe

Characterizing Distribution Equivalence and Structure Learning for Cyclic and Acyclic Directed Graphs [article]

AmirEmad Ghassami, Alan Yang, Negar Kiyavash, Kun Zhang
2020 arXiv   pre-print
in terms of the Markov equivalence.  ...  in the distribution that is useful for identification of the underlying structure.  ...  Acknowledgements This work was supported in part by ONR grant W911NF-15-1-0479, NSF CCF 1704970, and NSF CNS 16-24811.  ... 
arXiv:1910.12993v3 fatcat:vu2z7fp6x5e5vklrncbxtjkqhm
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