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

2020
*
arXiv
*
pre-print

We also prove

arXiv:2007.02834v1
fatcat:ognfd4yvonbfxjju5exanxm6im
*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. ...##
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Global Constraint Catalogue: Past, Present and Future

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 ...

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

2014
*
arXiv
*
pre-print

On the other hand, we observe that $W(G)\le 3\,\

arXiv:1312.5937v2
fatcat:uifjmirqhzgqzdejnz35r3ma6e
*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. ...##
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International Journal Of Mathematical Combinatorics, Vol.6
[article]

2012
*
Zenodo
*

The International J.Mathematical Combinatorics (ISSN 1937-1055) is

doi:10.5281/zenodo.8810
fatcat:6skpbiwt3jfsrkcv44sffouegi
*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. ...##
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A spanning union of cycles in rectangular grid graphs, thick grid cylinders and Moebius strips
[article]

2021
*
arXiv
*
pre-print

of

arXiv:2109.12432v2
fatcat:3vkilyms25bp5c2gyj5na37sem
*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). ...##
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Further Research on Node Based Bottleneck Improvement Problem for Multicut
[chapter]

2006
*
Lecture Notes in Computer Science
*

ECCO was started in 1987 by

doi:10.1007/11816157_107
fatcat:xjdnf4kesrbczoh4ilvxxixqei
*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 ...##
###
Dynamic functional connectivity

2007
*
Current Opinion in Neurobiology
*

As shown

doi:10.1016/j.conb.2007.03.008
pmid:17379500
fatcat:4msvaswltbcgpnlyggftheqcnm
*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. ...##
###
The Graph Theoretical Approach in Brain Functional Networks: Theory and Applications

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

doi:10.2200/s00279ed1v01y201004bme036
fatcat:cjfe6uqky5as3ff4f2z4usftii
*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. ...##
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JGraphT – A Java library for graph data structures and algorithms
[article]

2020
*
arXiv
*
pre-print

Besides classic graph algorithms such as shortest-paths and

arXiv:1904.08355v2
fatcat:vzv6n26i4fcohga7r5ww7exgay
*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. ...##
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Study and evaluation of an Irregular Graph Algorithm on Multicore and GPU Processor Architectures
[article]

2016
*
arXiv
*
pre-print

To the best of our knowledge, this algorithm

arXiv:1603.02655v1
fatcat:nklt3op66vdfdpmd3ygeckhwla
*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 }. ...##
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The integrality gap of the asymmetric travelling salesman problem

2013

This contrasts sharply

doi:10.20381/ruor-19875
fatcat:n4iiwrrdcnetdkdeiaoobsiaf4
*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*. ...##
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International Journal of Mathematical Combinatorics, vol. 1/2015

2018
*
Figshare
*

The International J.Mathematical Combinatorics (ISSN 1937-1055) is

doi:10.6084/m9.figshare.6198917
fatcat:toihd32iunggrjwvtd3wbji424
*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). ...##
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Why we live in hierarchies: a quantitative treatise
[article]

2017
*
arXiv
*
pre-print

This book is concerned

arXiv:1707.01744v1
fatcat:aaeb44rwinef5irdy2kzbwtqtq
*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. ...##
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Learning to Predict Combinatorial Structures
[article]

2010
*
arXiv
*
pre-print

The consequence is

arXiv:0912.4473v2
fatcat:olzo64uyxfg5jcjjvtjidvek54
*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). ...##
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Twenty Combinatorial Examples of Asymptotics Derived from Multivariate Generating Functions

2008
*
SIAM Review
*

Let {ar : r ∈

doi:10.1137/050643866
fatcat:xzp7nflc5ze3vaa2ryzbf5hi2u
*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. ...
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