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Neighborhood-Preserving Translations on Graphs [article]

Nicolas Grelier and Bastien Pasdeloup and Jean-Charles Vialatte and Vincent Gripon
2016 arXiv   pre-print
In this paper we are interested in defining translations on graphs using a few simple properties.  ...  Namely we propose to define translations as functions from vertices to adjacent ones, that preserve neighborhood properties of the graph.  ...  Let f be a geometrical translation on a cyclic grid graph G, then f is a perfect graphical translation on G.  ... 
arXiv:1606.02479v1 fatcat:jmwyoiwa6ngd7lrvamnaalnbka

Page 19 of Mathematical Reviews Vol. 43, Issue 1 [page]

1972 Mathematical Reviews  
The remainder of the paper is devoted to a more detailed study of two distinguished subclasses of matroids, one of which (the B-matroids) has properties closely analogous to those of matroids on finite  ...  It is also shown that if a graph gives rise to a matroid, then this matroid is a B-matroid [loc. cit.]. Author’s review (Zbl 195, 543) Sachs, David 82 Geometric mappings on geometric lattices. Canad.  ... 

Plane Geometric Graph Augmentation: A Generic Perspective [chapter]

Ferran Hurtado, Csaba D. Tóth
2012 Thirty Essays on Geometric Graph Theory  
We consider augmentation problems over plane geometric graphs, that is, graphs given with a crossing-free straight-line embedding in the plane.  ...  The geometric constraints on the possible new edges render some of the simplest augmentation problems intractable, and in many cases only extremal results are known.  ...  Spanning graphs with desirable properties In many applications, we do not necessarily want to embed a specific graph on top of a point set S, but rather we would like to construct a spanning graph on S  ... 
doi:10.1007/978-1-4614-0110-0_17 fatcat:vpjhqxc6qffe3h2tjjwzle6stq

Edge-Removal and Non-Crossing Configurations in Geometric Graphs

Oswin Aichholzer, Sergio Cabello, Ruy Fabila-Monroy, David Flores-Peñaloza, Thomas Hackl, Clemens Huemer, Ferran Hurtado, David R. Wood
2010 Discrete Mathematics & Theoretical Computer Science  
The non-crossing subgraphs that we consider are perfect matchings, subtrees of a given size, and triangulations. In each case, we obtain tight bounds on the maximum number of removable edges.  ...  Graphs and Algorithms International audience A geometric graph is a graph G = (V, E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints  ...  We prove that every complete geometric graph on 2n vertices still contains a non-crossing perfect matching after removing any set of n − 1 edges.  ... 
doi:10.46298/dmtcs.525 fatcat:2aevw6sqrbbm5bs6rxxmd5yveq

On the chromatic number of some flip graphs

Ruy Fabila-Monroy, David Flores-Peñaloza, Clemens Huemer, Ferran Hurtado, Jorge Urrutia, David R. Wood
2009 Discrete Mathematics & Theoretical Computer Science  
Graphs and Algorithms International audience This paper studies the chromatic number of the following four flip graphs (under suitable definitions of a flip): the flip graph of perfect matchings of a complete  ...  graph of even order, the flip graph of triangulations of a convex polygon (the associahedron), the flip graph of non-crossing Hamiltonian paths of a set of points in convex position, and the flip graph  ...  (A set of points in the plane is in convex position if it forms the vertex-set of a convex polygon.) We then consider the flip graph on the perfect matchings of a complete graph of even order.  ... 
doi:10.46298/dmtcs.460 fatcat:v64rq7fv5bh23em64clegx4z7m

Page 3822 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
Let P be a property of graphs.  ...  “There are two general approaches to this problem, the first one known as geometric symmetries on the basis of drawings, the other resting upon the graph-theoretical notion of graphs.  ... 

Pseudocodeword-Free Criterion for Codes with Cycle-Free Tanner Graph [article]

Wittawat Kositwattanarerk
2017 arXiv   pre-print
In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant  ...  Therefore, cycles are usually seen as the culprit of low-density parity-check (LDPC) codes.  ...  This work is supported by the Thailand Research Fund under Grant TRG5880116 and the Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand.  ... 
arXiv:1706.06648v1 fatcat:wcn5cdvy2vfxhk3q5c4q4ed7ji

Pseudocodeword-free criterion for codes with cycle-free Tanner graph

Wittawat Kositwattanarerk
2018 Designs, Codes and Cryptography  
In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant  ...  Therefore, cycles are usually seen as the culprit of low-density parity-check (LDPC) codes.  ...  This work is supported by the Thailand Research Fund under Grant TRG5880116 and the Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand.  ... 
doi:10.1007/s10623-018-0476-3 fatcat:xaq6yknd5bdc7dbrvq2zffqkxy

Page 72 of Mathematical Reviews Vol. , Issue 97A [page]

1997 Mathematical Reviews  
Here by ageometric property” is meant the requirement of a rich collection of subgraphs, each embedded within the graph in a restricted manner.  ...  paper: If G is a perfect Ks ~ {e}-free graph, at least one of the following statements is true: (a) G is bipartite or the line graph of a bipartite graph; (b) G has a separating clique; (c) G has a sep  ... 

Reduction of constraint systems [article]

Samy Ait-Aoudia, Roland Jegou, Dominique Michelucci
2014 arXiv   pre-print
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations.  ...  This paper also gives an efficient method to decompose well constrained systems into irreducible ones. These decompositions greatly speed up the resolution in case of reducible systems.  ...  Property 1. Consider any perfect matching M of G.  ... 
arXiv:1405.6131v1 fatcat:olmpysx27zbuvo2ek4ik6ipooy

Hybrid multiobjective optimization genetic algorithms for graph drawing

Dana Vrajitoru
2007 Proceedings of the 9th annual conference on Genetic and evolutionary computation - GECCO '07  
In this paper we introduce an application of multiobjective optimization with genetic algorithms to the problem of graph drawing and explore the potential contribution of the genetic algorithms for this  ...  ALGORITHMS AND RESULTS The problem we focus on for this study is building consistent graph layouts for weighted graphs, in particular following a specified geometric shape.  ...  The population size was of 50 or 100, depending on the size of the graph.  ... 
doi:10.1145/1276958.1277142 dblp:conf/gecco/Vrajitoru07 fatcat:y3dxbefczzfi3memztmzihplhm

Ramsey-Type Results for Unions of Comparability Graphs

Adrian Dumitrescu, Géza Tóth
2002 Graphs and Combinatorics  
Similar results are obtained for graphs which are a union of a fixed number k of comparability graphs. We also show that the same bounds hold for unions of perfect graphs.  ...  Given a graph on n vertices which is the union of two comparability graphs on the same vertex set, it always contains a clique or independent set of size n 1 3 .  ...  We prove the lower bound in the Theorem by induction on k. For k = 1, the statement is a direct consequence of the definition of perfect graphs.  ... 
doi:10.1007/s003730200017 fatcat:oyglnndkyzghpna2otd66qnocm

Experimental Study of Independent and Dominating Sets in Wireless Sensor Networks Using Graph Coloring Algorithms [chapter]

Dhia Mahjoub, David W. Matula
2009 Lecture Notes in Computer Science  
and a near-perfect node coverage yield.  ...  We also observe that in dense random deployments, certain coloring algorithms yield a packing of the nodes into independent sets each of which is relatively close to the perfect placement in the triangular  ...  Saeed Abu-Nimeh for several valuable discussions and Ilteris Murat Derici for his initial work on the SL algorithm and RGG.  ... 
doi:10.1007/978-3-642-03417-6_4 fatcat:hbvpocsncbcwhmic75suu76asq

Forthcoming papers

1991 Discrete Mathematics  
Simpson, Disjoint covering systems of rational Beatty sequences A rational Beatty sequence is a sequence {[on + /I]}, where (Y is rational, n runs through the integers and square brackets denote integer  ...  It is shown that the collection of all ('4) quadruples chosen from a set of eleven points can be partitioned into eleven mutually disioint 3-(10.4. 11 desiens in oreciselv 21 non-isomomhic wavn. R.J.  ...  Computer outputs throw light on the structure of Pascal's array modulo primes and prime powers. The geometrical picture gives new meaning to relations known before and reveals new properties.  ... 
doi:10.1016/0012-365x(91)90052-4 fatcat:3g4xmr656vaczdgn4xzyl6d6ra

Perfect quantum state transfer on diamond fractal graphs [article]

Maxim Derevyagin, Gerald V. Dunne, Gamal Mograby, Alexander Teplyaev
2020 arXiv   pre-print
We use methods from fractal analysis and probability to find a new class of quantum spin chains on fractal-like graphs (known as diamond fractals) which support perfect quantum state transfer, and which  ...  have a wide range of different Hausdorff and spectral dimensions.  ...  This research was supported in part by the University of Connecticut Research Excellence Program, by DOE grant DE-SC0010339 and by NSF DMS grants 1613025 and 2008844.  ... 
arXiv:1909.08668v2 fatcat:xypmoitc5rh3jc2yewa3ngffla
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