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Ramsey numbers of graphs with long tails

1982
*
Discrete Mathematics
*

to an arbitrary n~~t~bipartit~

doi:10.1016/0012-365x(82)90017-6
fatcat:sp22adlo7jd4fjjdw3dawwmyc4
*graph*with a*long**path*f'tail"i ~~lanat~ng from one*of*its points. ... While*the*classical ramsey*numbers*r(K,,, K,,1) seem beyond computation for all but*very*small values*of*n and m, much progress has been made [4] in determining ramsey*numbers**of*sparser*graphs*, such ...##
###
Explicit construction of linear sized tolerant networks

1988
*
Discrete Mathematics
*

*graph*still

*contains*a

*path*

*of*length m. ... This settles a problem

*of*Rosenberg, which was motivated by

*the*study

*of*fault tolerant linear arrays. ... Introduction What is

*the*minimum possible

*number*

*of*vertices and edges

*of*a

*graph*G, such that even after removing all but portion

*of*its vertices or edges,

*the*remaining

*graph*still

*contains*a

*path*

*of*...

##
###
Explicit construction of linear sized tolerant networks

2006
*
Discrete Mathematics
*

*graph*still

*contains*a

*path*

*of*length m. ... This settles a problem

*of*Rosenberg, which was motivated by

*the*study

*of*fault tolerant linear arrays. ... Introduction What is

*the*minimum possible

*number*

*of*vertices and edges

*of*a

*graph*G, such that even after removing all but portion

*of*its vertices or edges,

*the*remaining

*graph*still

*contains*a

*path*

*of*...

##
###
Explicit Construction of Linear Sized Tolerant Networks
[chapter]

1988
*
Annals of Discrete Mathematics
*

*graph*still

*contains*a

*path*

*of*length m. ... This settles a problem

*of*Rosenberg, which was motivated by

*the*study

*of*fault tolerant linear arrays. ... Introduction What is

*the*minimum possible

*number*

*of*vertices and edges

*of*a

*graph*G, such that even after removing all but portion

*of*its vertices or edges,

*the*remaining

*graph*still

*contains*a

*path*

*of*...

##
###
On large induced trees and long induced paths in sparse random graphs

1992
*
Journal of combinatorial theory. Series B (Print)
*

Also, if L, denotes

doi:10.1016/0095-8956(92)90021-o
fatcat:phkhtc3m65gexiuvt6kc3u3so4
*the*length*of**the*longest*induced**path*in Gn,p, then we find a*number*h(c) such that L, is almost surely larger than (h(c) -E)n for any E>O. ... Let T" be*the*order*of**the*largest*induced*subtree*of*G, p' We find a*number*t(c) such that T" is almost surely larger than (t(c) -&)n for any E > 0. ... INTRODUCTION AND MAIN RESULTS This paper is concerned with*the**number**of*vertices in*the*largest*induced*trees and*the*length*of**the*longest*induced**paths*in*the*well-known random*graph*G,, P. ...##
###
Estimating graph distance and centrality on shared nothing architectures

2014
*
Concurrency and Computation
*

Computing

doi:10.1002/cpe.3354
fatcat:boqyj6pnibeb5frkqgc5sizqay
*the*exact shortest*paths*between a large*number**of*vertices is a costly operation, and serial algorithms are not practical for billion-scale*graphs*. ... Our method exploits data locality, produces highly accurate results, and allows batch computation*of*shortest*paths*with 7% average error in*graphs*that*contain*billions*of*edges. ...*The*size*of**the**induced**graph*is O.kD/, and*the**estimation*algorithm runs in at most O.k 2 D 2 / time for a pair*of*vertices. ...##
###
Page 4877 of Mathematical Reviews Vol. , Issue 89I
[page]

1989
*
Mathematical Reviews
*

Specifically,

*the*following characteristics are studied:*the*lengths*of**the*longest cycle and*the*longest*path*,*the*total*number**of*vertices in*the*unicyclic components and total*number**of*vertices forming ... Moreover,*the*subgraph*of*a Ptolemy*graph**induced*by*the*set*of*vertices having*the*maximal distance is a union*of*complete*graphs*. ...##
###
Path Sampling: A Fast and Provable Method for Estimating 4-Vertex Subgraph Counts
[article]

2014
*
arXiv
*
pre-print

Our algorithm is based on a novel technique

arXiv:1411.4942v1
fatcat:n6tztzp46beq7mlaugyxrgw5xu
*of*3-*path*sampling and a special pruning scheme to decrease*the*variance in*estimates*. ... We provide theoretical proofs for*the*accuracy*of*our algorithm, and give formal bounds for*the*error and confidence*of*our*estimates*. ... So X is 1 iff*the*th call to sample outputs a 3-*path**contained*in a copy*of**the*ith motif.*The*total*number**of*(distinct) such 3-*paths*is exactly A2,i · Ci. ...##
###
Economic Genome Assembly from Low Coverage Illumina and Nanopore Data

2020
*
Workshop on Algorithms in Bioinformatics
*

In

doi:10.4230/lipics.wabi.2020.10
dblp:conf/wabi/GatterLDHS20
fatcat:zkrxlttmkrdtzir55c4onqp2j4
*the*next step, properties*of*proper interval*graphs*are used to extract contigs as maximum weight*paths*. These are translated into genomic sequences only in*the*final step. ... LazyB starts from a bipartite overlap*graph*between*long*reads and restrictively filtered short-read unitigs, which are then reduced to a*long*-read overlap*graph*G. ... In fact, F △ is an*induced**path*in*the*triangle reduction H △*of*H. This deduction suggests to identify maximal*paths*in*the*triangle reduction ⇀ G △*of**the*directed acycling*graph*⇀ G as contigs. ...##
###
Travel Planning with Self-Made Maps
[chapter]

2001
*
Lecture Notes in Computer Science
*

To facilitate

doi:10.1007/3-540-44808-x_10
fatcat:wxekfxob3jcofbdiagszjz2udq
*the*use*of*such techniques when coordinates are missing from some, or even all,*of**the*nodes in a network we generate artificial coordinates using methods from*graph*drawing. ... Experiments on a large set*of*German train timetables indicate that*the*speed-up achieved with coordinates from our network drawings is close to that achieved with*the*actual coordinates. ... For realistic data,*the*total*number**of*springs thus introduced is linear in*the**number**of*vertices.*Long*-range dependencies. ...##
###
Lightning Fast and Space Efficient k-clique Counting

2022
*
Proceedings of the ACM Web Conference 2022
*

*number*

*of*k-cliques in

*the*dense regions

*of*

*the*

*graph*. ... Existing exact k-clique counting algorithms are often hard to handle large dense

*graphs*, while sampling-based solutions either require a huge

*number*

*of*samples or consume

*very*high storage space to achieve ... Rong-Hua Li is

*the*corresponding author

*of*this paper. ...

*The*need for indexing massive

*graphs*is an urgent research problem

*of*great practical importance.

*The*main challenge is

*the*size. Each

*graph*may

*contain*at least tens

*of*millions vertices. ...

*Graphs*can represent a large

*number*

*of*data types, e.g., online social networks, internet links, procedure dependency

*graphs*, etc. ... Also, we select those

*induced*subgraphs

*of*

*the*database

*graph*as query

*graphs*. ...

##
###
A branch and bound algorithm for the robust shortest path problem with interval data

2004
*
Operations Research Letters
*

for each possible conÿguration

doi:10.1016/j.orl.2003.08.002
fatcat:cpq4lhxscfcn7dxuvflii7amv4
*of**the*arc costs. ... Many real problems can be modelled as robust shortest*path*problems on interval digraphs, where intervals represent uncertainty about real costs and a robust*path*is not too far from*the*shortest*path*... They have*very**long**paths*from s to t (each*path*visits a*number**of*vertices equal to*the**number**of*layers*of**the**graph*) and there is a huge*number**of*alternative*paths*from s to t, since between two consecutive ...##
###
Combinatorics and algorithms for augmenting graphs
[article]

2014
*
arXiv
*
pre-print

However, our knowledge

arXiv:1410.8774v1
fatcat:ubvuow4oenhy7f7ix2t2fnywim
*of*augmenting*graphs*is still*very*limited, and we do not even know what*the*minimal infinite classes*of*augmenting*graphs*are. ...*The*notion*of*augmenting*graphs*generalizes Berge's idea*of*augmenting chains, which was used by Edmonds in his celebrated solution*of**the*maximum matching problem. ...*The*support*of*EPFL is gratefully acknowledged. ...##
###
Embedding nearly-spanning bounded degree trees

2007
*
Combinatorica
*

We derive a sufficient condition for a sparse

doi:10.1007/s00493-007-2182-z
fatcat:5khyhmyixjhdzdjb2j3bjwkhaa
*graph*G on n vertices to*contain*a copy*of*a tree T*of*maximum degree at most d on (1 − )n vertices, in terms*of**the*expansion properties*of*G. ... We also prove that if an (n, D, λ)-*graph*G (i.e., a D-regular*graph*on n vertices all*of*whose eigenvalues, except*the*first one, are at most λ in their absolute values) has large enough spectral gap D ... They would like to thank*the*members*of**the*Theory Group at Microsoft Research for their hospitality and for creating a stimulating research environment. ...
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