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On a 2-factor with a specified edge in a graph satisfying the Ore condition

Atsushi Kaneko, Kiyoshi Yoshimoto
2002 Discrete Mathematics  
In this article, we prove that if 2(G) ¿ |V (G)|, then for an edge e of G, there exists a 2-factor with k cycles that contains e, or |V (G)| is even and G has a vertex cover of size |V (G)|=2 containing  ...  Let k be an integer greater than one, and let G be a simple graph with at least 4k + 1 vertices.  ...  Acknowledgements The authors wish to thank Dr. Y. Ishigami for his helpful advices and anonymous referees for appropriate comments.  ... 
doi:10.1016/s0012-365x(02)00506-x fatcat:4qzp6yswpfdxnkxnuvplp7xi6a

Graphical models in Macaulay2 [article]

Luis David García-Puente, Sonja Petrović, Seth Sullivant
2013 arXiv   pre-print
graphs, and for checking for identifiable parameters in Gaussian mixed graph models.  ...  The Macaulay2 package GraphicalModels contains algorithms for the algebraic study of graphical models associated to undirected, directed and mixed graphs, and associated collections of conditional independence  ...  Work on the package was carried out during the 2010 and 2011 Macaulay2 workshops, which were partially supported by the US National Science Foundation and the Institute for Mathematics and Its Applications  ... 
arXiv:1208.6550v3 fatcat:5vi7572f6bgsvpavxwcsswxscu

Graphical models

Luis García-Puente, Sonja Petrović, Seth Sullivant
2013 The Journal of Software for Algebra and Geometry  
graphs, and for checking for identifiable parameters in Gaussian mixed graph models.  ...  The Macaulay2 package GraphicalModels contains algorithms for the algebraic study of graphical models associated to undirected, directed and mixed graphs, and associated collections of conditional independence  ...  There are two natural ways to specify a graphical model, through either conditional independence statements specified by the graph or via a parametric representation (often called a "factorization").  ... 
doi:10.2140/jsag.2013.5.1 fatcat:vjnij3nyznc4tddxtcoffgylba

A factoring algorithm using polygon-to-chain reductions for computing K-terminal network reliability

R. Kevin Wood
1985 Networks  
Let G = (V,E) be an undirected graph whose edges may fail, and let G, denote G with a set K V specified. Edge failures are assumed to be statistically independent and to have known probabilities.  ...  Removing the restriction on edge selection leaves results essentially unchanged in the upper range of IK(, but minimum domination becomes only a tight upper bound for the lower range. analyze the complexity  ...  Then, under the same conditions we show that an optimal edge-selection strategy can be specified when 2 I IKI 5 151 or IVI -2 5 IKI 5 IVI.  ... 
doi:10.1002/net.3230150204 fatcat:ph2ispuervdvtkpk2ngpgidafe

A look at cycles containing specified elements of a graph

Ronald J. Gould
2009 Discrete Mathematics  
edges of specified size, a set of independent edges satisfying a specified property, a set of disjoint paths containing a fixed number of edges, a combination of vertices and edges, or a linear forest  ...  One possibility is to ask any of these questions in a fixed special class of graphs like planar graphs or hypercubes. For lack of space, we shall not concentrate on these questions here.  ...  Acknowledgements The author would like to thank the referees for their very helpful comments.  ... 
doi:10.1016/j.disc.2008.04.017 fatcat:uzmzlcs6lvdzjaf5nd55wmysjm

Compatible 2-factors

Jan Kratochvil, Svatopluk Poljak
1992 Discrete Applied Mathematics  
Given a graph G and, at each vertex o, a set of pairs of edges incident to I, (called allowed transitions), a 2-factor Fof G is called compatible (with the transition system) if for each vertex u, the  ...  Such a 2-factor F is called compatibie with T= (T(U), v E V) (briefly a compatible 2-factor).  ...  Acknowledgement The authors would like to thank the referees for valuable comments and suggestions, leading in particular to simplification of the proofs of Lemma 4.1 and Theorem 6. I.  ... 
doi:10.1016/0166-218x(92)90257-b fatcat:6n556d5al5d7xf4amcjf4khn24

Knowledge representation and update in hierarchies of graphs [article]

Russ Harmer, Eugenia Oshurko
2020 arXiv   pre-print
The implementation of this theory, in the ReGraph Python library for (simple) directed graphs with attributes on nodes and edges, is then discussed in the context of two significant use cases.  ...  The conditions under which knowledge update, in the form of the sesqui-pushout rewriting of an object in a hierarchy, can be propagated to the rest of the hierarchy, in order to maintain all required path  ...  of the hierarchy in such a way that the commutativity condition is satisfied.  ... 
arXiv:2002.01766v1 fatcat:7e3a2ashsjekfa73tojj7xkoom

Low-dimensional embedding with extra information

Mihai Bǎdoiu, Erik D. Demaine, Mohammad Taghi Hajiaghayi, Piotr Indyk
2004 Proceedings of the twentieth annual symposium on Computational geometry - SCG '04  
More precisely, we are given a graph, the approximate lengths of the edges, and possibly extra information, and our goal is to assign coordinates to the vertices that satisfy the given constraints up to  ...  a constant factor away from the best possible.  ...  LEMMA 8 . 8 Given a graph G with edge lengths specified by D, we can check in polynomial time whether there is an embedding f that satisfies the range condition and matches D exactly on the edges of f  ... 
doi:10.1145/997817.997866 dblp:conf/compgeom/BadoiuDHI04 fatcat:f7j6hlcsgbgvjc4yolpbwfx3ay

MAP Estimation Via Agreement on Trees: Message-Passing and Linear Programming

M.J. Wainwright, T.S. Jaakkola, A.S. Willsky
2005 IEEE Transactions on Information Theory  
We develop and analyze methods for computing provably optimal maximum a posteriori probability (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles.  ...  In this way, we establish a connection between a certain LP relaxation of the mode-finding problem and a reweighted form of the max-product (min-sum) message-passing algorithm.  ...  ACKNOWLEDGMENT The authors wish to thank Jon Feldman and David Karger for helpful discussions.  ... 
doi:10.1109/tit.2005.856938 fatcat:uovgjk2a5bddtcuga2wo7erure

Generic pole assignability, structurally constrained controllers and unimodular completion

Rachel K. Kalaimani, Madhu N. Belur, Sivaramakrishnan Sivasubramanian
2013 Linear Algebra and its Applications  
J.W. van der Woude for discussions in the context of Theorem 2.7. We also thank Dr. Fan Yang for pointing corrections in a preliminary version.  ...  matrix satisfies certain 'homogeneity conditions' on its invariant factors: the factors are assumed to be monomials.  ...  to this edge is a polynomial of degree one or more.  ... 
doi:10.1016/j.laa.2013.10.004 fatcat:yjf6mlwi5fbdfe3xphrgxmve5a

The structure and existence of 2-factors in iterated line graphs

Michael J. Ferrara, Ronald J. Gould, Stephen G. Hartke
2007 Discussiones Mathematicae Graph Theory  
Specifically, we give degree conditions on G that ensure L 2 (G) contains a 2-factor with every possible number of cycles, and we give a sufficient condition for the existence of a 2-factor in L 2 (G)  ...  We prove several results about the structure of 2-factors in iterated line graphs.  ...  We also give a sufficient condition for the existence of a 2-factor in L 2 (G) with all cycle lengths specified.  ... 
doi:10.7151/dmgt.1376 fatcat:jaflokhiknfvzhkxm5tjfplhfa

Factoring Algorithms for Computing K-Terminal Network Reliability

R. Kevin Wood
1986 IEEE Transactions on Reliability  
math needed to use results: Same Results useful to: Reliability analysts and theoreticians Abstract-Let GK denote a graph G whose edges can fail and with a set K C V specified.  ...  A factoring algorithm for computing network reliability recursively applies the formula R(GK) = piR(GK * eC) + qiR(GKe) where GK * ec is GK, with edge ec contracted, GjKei is GK with e deleted andpi m  ...  R7 is general, and is the dual of a type 1 polygon-to-chain reduction in a planar graph with KI = 2. R8 is trivially derived by factoring on the edge ea, hence its name.  ... 
doi:10.1109/tr.1986.4335431 fatcat:xkrrloaqdjeubowd65hjybjhz4

Low-Dimensional Embedding with Extra Information

Mihai Badoiu, Erik D. Demaine, MohammadTaghi Hajiaghayi, Piotr Indyk
2006 Discrete & Computational Geometry  
or additive) error on the resulting distances and other information is within a constant factor of the best possible.  ...  For general graphs, the analogous problem is NP-hard even with exact distances.  ...  Acknowledgments We thank the anonymous referees for their helpful comments.  ... 
doi:10.1007/s00454-006-1268-5 fatcat:7lr2eqtxzzdzdop6dzhzyicpsy

Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs [article]

Armen S. Asratian, Carl Johan Casselgren (Umea University), Jennifer Vandenbussche, Douglas B. West
2007 arXiv   pre-print
An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive.  ...  A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings.  ...  On the other hand, (3, 4) -biregular bigraphs with multiple edges need not have proper path-factors, even if they satisfy Pyatkin's condition.  ... 
arXiv:0704.2650v1 fatcat:dnotowwggnejhiyy3hqd2gol3e

The Ponzano-Regge model and Reidemeister torsion [article]

John W. Barrett, Ileana Naish-Guzman
2006 arXiv   pre-print
The Ponzano-Regge model of three-dimensional quantum gravity is well-defined when the observables satisfy a certain condition involving the twisted cohomology.  ...  In this case, the partition function is defined in terms of the Reidemeister torsion. Some consequences for the special cases of planar graphs and knots are given.  ...  To specify an observable, we need a graph embedded in M, and some data on each edge of the graph. More precisely, let Γ be a connected subcomplex consisting of edges and vertices of M.  ... 
arXiv:gr-qc/0612170v1 fatcat:no3sj74xsbhs3pburxkohlkvem
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