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Non-separating spanning trees and out-branchings in digraphsof independence number 2 [article]

Joergen Bang-Jensen, Stéphane Bessy, Anders Yeo
2020 arXiv   pre-print
We also prove a number of other results, including that every 2-arc-strong digraph D with alpha(D)<=2 and at least 14 vertices has a non-separating spanning tree and that every graph G with delta(G)>=4  ...  Our main results are that every 2-arc-strong digraph D of independence number alpha(D) = 2 and minimum in-degree at least 5 and every 2-arc-strong oriented graph with alpha(D) = 2 and minimum in-degree  ...  The main result here is Theorem 23 which says that every 2-arc-strong digraph D with α(D) = 2 and n ≥ 14 vertices has a non-separating spanning tree.  ... 
arXiv:2007.02834v1 fatcat:ognfd4yvonbfxjju5exanxm6im

Global Constraint Catalogue: Past, Present and Future

Nicolas Beldiceanu, Mats Carlsson, Sophie Demassey, Thierry Petit
2007 Constraints  
A number of possible enhancements are proposed as well as several research paths for the development of the area. potential use of a global constraint.  ...  From an early time, global constraints have been used for their strong pruning power thanks to efficient specialised filtering algorithms that take advantage of the structure of the constraints they consider  ...  Renormalise − → G (X T U , E T U ) according to the fact that the final digraph has to be symmetric. c) u is the extremity of a T -arc and v is saturated in every maximum matching in the subgraph induced  ... 
doi:10.1007/s10601-006-9010-8 fatcat:ko7zyu7b7vczvb3wyyeauzvy2i

On the dynamic width of the 3-colorability problem [article]

Albert Atserias, Anuj Dawar, Oleg Verbitsky
2014 arXiv   pre-print
On the other hand, we observe that $W(G)\le 3\,\alpha(G)+1$ and $W(G)\le n-\alpha(G)+1$ for every non-3-colorable graph $G$ with $n$ vertices, where $\alpha(G)$ denotes the independence number of $G$.  ...  The last condition can be checked by a $k$-consistency algorithm where the parameter $k$ has to be chosen large enough, dependent on $G$.  ...  If n > 4, Spoiler uses a standard separator strategy. Every tree T with n vertices has a single-vertex separator, that is, a vertex v such that every component of T − v has at most n/2 vertices.  ... 
arXiv:1312.5937v2 fatcat:uifjmirqhzgqzdejnz35r3ma6e

International Journal Of Mathematical Combinatorics, Vol.6 [article]

Mao, Linfan (Editor-in-Chief)
2012 Zenodo  
The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising  ...  N. Prasad for their invaluable suggestions and criticisms also. Also author V. K.  ...  Chaubey is very much thankful to NBHM-DAE of Goverment of INDIA for their financial assistance as a Postdoctoral Fellowship.  ... 
doi:10.5281/zenodo.8810 fatcat:6skpbiwt3jfsrkcv44sffouegi

A spanning union of cycles in rectangular grid graphs, thick grid cylinders and Moebius strips [article]

Jelena Djokić, Olga Bodroža-Pantić, Ksenija Doroslovački
2021 arXiv   pre-print
of spanning unions of cycles, the so-called 2-factors, in these graphs (as a generalizations of HCs).  ...  For all the three types of graphs from the title and for any integer m ≥ 2 we propose an algorithm for obtaining a specially designed (transfer) digraph D^*_m.  ...  A 2-factor of M S m (n) can have at most one short nc-type cycle (due to topological reasons, too).  ... 
arXiv:2109.12432v2 fatcat:3vkilyms25bp5c2gyj5na37sem

Further Research on Node Based Bottleneck Improvement Problem for Multicut [chapter]

Xiucui Guan, Jie Su
2006 Lecture Notes in Computer Science  
ECCO was started in 1987 by a group of leading experts in Operations Research and Management Science.  ...  ECCO wants to provide a forum for researchers in combinatorial optimization, either in its theoretical aspects or in business, industry or public administration applications.  ...  The p-Center problem consists in locating p facilities among a set of M possible locations and assigning N clients to them in order to minimize the maximum distance between a client and the facility to  ... 
doi:10.1007/11816157_107 fatcat:xjdnf4kesrbczoh4ilvxxixqei

Dynamic functional connectivity

Andreas A Ioannides
2007 Current Opinion in Neurobiology  
As shown at the end of this review, a correspondence principle can be formulated to guide the interpretation across network levels and to relate nodes to well defined anatomical entities.  ...  a hierarchy of networks rather than the single, binary networks that are currently in vogue.  ...  Acknowledgements The figures in the review rely on research conducted by AAI with Drs Lichan Liu, Vahe Poghosyan and Masaki Maruyama.  ... 
doi:10.1016/j.conb.2007.03.008 pmid:17379500 fatcat:4msvaswltbcgpnlyggftheqcnm

The Graph Theoretical Approach in Brain Functional Networks: Theory and Applications

Fabrizio De Vico Fallani, Fabio Babiloni
2010 Synthesis Lectures on Biomedical Engineering  
Lectures in Biomedical Engineering will be comprised of 75-to 150-page publications on advanced and state-of-the-art topics that spans the field of biomedical engineering, from the atom and molecule to  ...  Moreover, the fact that these patterns occur at multiple frequencies support the evidence that brain functional networks contain multiple frequency channels along which information is transmitted.  ...  Acknowledgments We wish to thank Donatella Mattia, Febo Cincotti, and Laura Astolfi for their kind support and for being a constant source of challenging ideas.  ... 
doi:10.2200/s00279ed1v01y201004bme036 fatcat:cjfe6uqky5as3ff4f2z4usftii

JGraphT – A Java library for graph data structures and algorithms [article]

Dimitrios Michail and Joris Kinable and Barak Naveh and John V Sichi
2020 arXiv   pre-print
Besides classic graph algorithms such as shortest-paths and spanning-tree algorithms, the library contains numerous advanced algorithms: graph and subgraph isomorphism; matching and flow problems; approximation  ...  One such package is JGraphT, a programming library which contains very efficient and generic graph data-structures along with a large collection of state-of-the-art algorithms.  ...  A complete list of all contributors, as well as their contributions, can be found at the project's GitHub 13 page.  ... 
arXiv:1904.08355v2 fatcat:vzv6n26i4fcohga7r5ww7exgay

Study and evaluation of an Irregular Graph Algorithm on Multicore and GPU Processor Architectures [article]

Varun Nagpal
2016 arXiv   pre-print
To the best of our knowledge, this algorithm has only been accelerated on supercomputer class computer named Cray XMT and no work exists that demonstrates performance evaluation and comparison of this  ...  A triad is defined as a digraph with 3 vertices and zero or more arcs connecting them. Similar to triad, a dyad is a pair of vertices which have zero or more arcs between them.  ...  Consider a strict digraph (no loops) G = [V, E] where V = {1, 2...n} is set of vertices and E ⊆ V x V the set of arcs (directed) i.e. E = {(u, v), ∃u, v ∈ V }.  ... 
arXiv:1603.02655v1 fatcat:nklt3op66vdfdpmd3ygeckhwla

The integrality gap of the asymmetric travelling salesman problem

Paul Elliott-Magwood, Université D'Ottawa / University Of Ottawa, Université D'Ottawa / University Of Ottawa
2013
This contrasts sharply with the symmetric case with metric costs where a 32 -approximation algorithm is known and the integrality gap has been shown to be at most 3/2.  ...  The integrality gap gives a measure of the "goodness" of this lower bound; moreover, a constructive proof showing this integrality gap is at most some constant alpha would provide an alpha-approximation  ...  In order to accomplish this, we note that the support digraph of every half-integer extreme point has the property that every node has indegree and outdegree at most 2.  ... 
doi:10.20381/ruor-19875 fatcat:n4iiwrrdcnetdkdeiaoobsiaf4

International Journal of Mathematical Combinatorics, vol. 1/2015

Linfan Mao
2018 Figshare  
The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising  ...  Also, it is clear that every minimal x-monophonic set of G contains at most c elements and hence m + x (G) ≤ c.  ...  The following theorem shows that on removal of an edge in G, AD ie (G) can decrease by at most one and increase by at most 2. Theorem 3.3 Let G be a connected graph, e = uv ∈ E(G).  ... 
doi:10.6084/m9.figshare.6198917 fatcat:toihd32iunggrjwvtd3wbji424

Why we live in hierarchies: a quantitative treatise [article]

Anna Zafeiris, Tamás Vicsek
2017 arXiv   pre-print
This book is concerned with the various aspects of hierarchical collective behaviour which is manifested by most complex systems in nature.  ...  From the many of the possible topics, we plan to present a selection of those that we think are useful from the point of shedding light from very different directions onto our quite general subject.  ...  The cardinality of the feedback arc set found by this heuristic is at most M/2-N/6 where M is the number of edges and N is the number of vertices. Another heuristic is as follows.  ... 
arXiv:1707.01744v1 fatcat:aaeb44rwinef5irdy2kzbwtqtq

Learning to Predict Combinatorial Structures [article]

Shankar Vembu
2010 arXiv   pre-print
The consequence is a generalisation of the classical ridge regression for structured prediction. (ii) The second assumption is that a particular sampling problem can be solved efficiently.  ...  The consequence is a new technique for designing and analysing probabilistic structured prediction models.  ...  chain from its stationary distribution π β i is at most ǫ/5l exp(2/p).  ... 
arXiv:0912.4473v2 fatcat:olzo64uyxfg5jcjjvtjidvek54

Twenty Combinatorial Examples of Asymptotics Derived from Multivariate Generating Functions

Robin Pemantle, Mark C. Wilson
2008 SIAM Review  
Let {ar : r ∈ N d } be a d-dimensional array of numbers for which the generating function F (z) := r arz r is meromorphic in a neighborhood of the origin.  ...  The remainder of the survey focuses on combinatorial applications, such as enumeration of words with forbidden substrings, edges and cycles in graphs, polyominoes, and descents in permutations.  ...  Many thanks to Manuel Lladser and Alex Raichev for a number of comments on preliminary drafts.  ... 
doi:10.1137/050643866 fatcat:xzp7nflc5ze3vaa2ryzbf5hi2u
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