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Page 5935 of Mathematical Reviews Vol. , Issue 99i
[page]

1999
*
Mathematical Reviews
*

*of*G

*and*J denotes

*the*all-

*ones*matrix. ... Summary: “A (d,k)-

*digraph*is a regular directed

*graph*

*of*degree d> 1, diameter k > 1,

*and*order

*one*less than

*the*(unattained) Moore bound. ...

##
###
Generating connected acyclic digraphs uniformly at random

2004
*
Information Processing Letters
*

This algorithm is an extension

doi:10.1016/j.ipl.2003.06.002
fatcat:vlxbc4ppu5ge5cvozdmlfbppfq
*of*a previous*one*, designed to generate acyclic*digraphs*, non-necessarily*connected*. ... We describe a simple algorithm based*on*a Markov chain process to generate simply*connected*acyclic directed*graphs*over a fixed set*of*vertices. ... For sake*of*clarity, we denote by A*the*set*of*all*connected*acyclic*digraphs**and*modify*the*transition rules as follows. Take uniformly at*random*(i, j ) in V 2 . ...##
###
Hochschild homology, and a persistent approach via connectivity digraphs
[article]

2022
*
arXiv
*
pre-print

To extend them to higher degrees, we introduce

arXiv:2204.00462v1
fatcat:5wzkv7v6kbfjpjxiuxy4lbwu6a
*the*notion*of**connectivity**digraphs**and*analyse two main examples;*the*first, arising from Atkin's q-*connectivity*,*and**the*second, here called n-path*digraphs*... , generalising*the*classical notion*of*line*graphs*. ... Acknowledgements*The*authors acknowledge support from*the*École Polytechnique Fédérale de Lausanne via a collaboration agreement with*the*University*of*Aberdeen*and*wish to thank Ran Levi for his support ...##
###
Generating connected acyclic digraphs uniformly at random
[article]

2004
*
arXiv
*
pre-print

This algorithm is an extension

arXiv:cs/0403040v1
fatcat:73cdb2sutrhk3ooepnsq24vutq
*of*a previous*one*, designed to generate acyclic*digraphs*, non necessarily*connected*. ... We describe a simple algorithm based*on*a Markov chain process to generate simply*connected*acyclic directed*graphs*over a fixed set*of*vertices. ...*The*chain*M*′ is irreducible, that is, given two*connected*acyclic*digraphs*G*and*H, there exists in*M*′ a sequence*of*transitions Recall that a circuit in a directed*graph*G is a sequence*of*vertices ...##
###
Orbits of rotor-router operation and stationary distribution of random walks on directed graphs

2015
*
Advances in Applied Mathematics
*

In this paper we prove that all orbits

doi:10.1016/j.aam.2015.06.006
fatcat:bcz5dfs745eyflt67ebegz7key
*of**the*rotor-router operation have*the*same size*on*a strongly*connected*directed*graph*(*digraph*)*and*give a formula for*the*size. ... It turns out that*on*a strongly*connected**digraph**the*stationary distribution*of**the*simple*random*walk coincides with*the*frequency*of*vertices in a rotor walk. ... Levine*and**M*. Farrell for their useful comments*on**the*paper. ...##
###
The birth of the contradictory component in random 2-SAT
[article]

2019
*
arXiv
*
pre-print

This follows from

arXiv:1904.10266v1
fatcat:4inbubamozcizamt65w5qyp5jq
*the*relation between these kernels*and**the*complex component*of*a*random**graph*in*the*subcritical phase. ... This partly settles*the*question about*the*structural similarity between*the*phase transitions in 2-SAT*and**random**graphs*. ...*The*author is indebted toÉlie de Panafieu*and*Vlady Ravelomanana for uncountable very inspiring discussions*and*for their support*and*encouragement. ...##
###
Maximum directed cuts in acyclic digraphs

2007
*
Journal of Graph Theory
*

We investigate

doi:10.1002/jgt.20215
fatcat:yk4lc6wug5drfm24new6zf5rfa
*the*size*of**the*largest directed cut in acyclic*digraphs*,*and*prove a number*of*related results concerning cuts in*digraphs**and*acyclic*digraphs*. ... It is easily shown that every*digraph*with*m*edges has a directed cut*of*size at least*m*/4,*and*that 1/4 cannot be replaced by any larger constant. ... Let D be an acyclic*digraph*with*m*edges. Identifying*one*vertex from each component, we may assume that*the*underlying*graph**of*D is*connected*. ...##
###
Sizing the length of complex networks
[article]

2018
*
arXiv
*
pre-print

*The*representation here introduced frees network comparison from

*the*need to rely

*on*

*the*choice

*of*reference

*graph*models (e.g.,

*random*

*graphs*

*and*ring lattices), a common practice that is prone to yield ... For that, we first had to uncover

*the*upper

*and*

*the*lower limits for

*the*pathlength

*and*efficiency, which indeed depend

*on*

*the*specific number

*of*nodes

*and*links. ... no

*connected*

*random*

*graphs*could be constructed

*of*same N

*and*L. ...

##
###
Page 5473 of Mathematical Reviews Vol. , Issue 98I
[page]

1998
*
Mathematical Reviews
*

*the*

*orientations*

*of*a

*graph*. ... Finally, we show that

*the*probability a

*random*

*oriented*

*graph*has an EDS is exponentially small when such a

*graph*is chosen according to a uniform distribution.” Douglas F. ...

##
###
On uniform sampling simple directed graph realizations of degree sequences
[article]

2009
*
arXiv
*
pre-print

It has been shown in

arXiv:0912.3834v1
fatcat:btygwyiiljdwdemtxh4idkcl4a
*the*past that*one*can perform a Markov chain arc-switching algorithm to sample a simple directed*graph*uniformly by performing two types*of*switches: a 2-switch*and*a directed 3-cycle ... In particular,*the*class*of*degree sequences where this is required is a subclass*of**the*directed 3-cycle anchored degree sequences. ... This work was funded by*the*postdoctoral*and*undergraduate biological sciences education program grant awarded to*the*College*of*William*and*Mary by*the*Howard Hughes Medical Institute. ...##
###
Extremal results on feedback arc sets in digraphs
[article]

2022
*
arXiv
*
pre-print

*The*proof uses a

*connection*to Turán numbers

*and*a result

*of*Bukh

*and*Conlon. ... A simple consequence

*of*a result

*of*Berger

*and*Shor is that any

*oriented*

*graph*G with

*m*edges satisfies β(G) =

*m*/2 - Ω(

*m*^3/4). ...

*The*proof

*of*Theorem 1.5 uses a

*random*

*orientation*

*of*any undirected

*graph*that is B-free with n vertices

*and*with

*m*= ex(n, B) edges. ...

##
###
A survey on Hamilton cycles in directed graphs
[article]

2010
*
arXiv
*
pre-print

We survey some recent results

arXiv:1006.0590v1
fatcat:vayfrvmx2vba7fnbrhoriu2dxq
*on*long-standing conjectures regarding Hamilton cycles in directed*graphs*,*oriented**graphs**and*tournaments. ... We also highlight*the*role that*the*notion*of*'robust expansion' plays in several*of**the*proofs. New*and*old open problems are discussed. ... Acknowledgements We are grateful to Demetres Christofides, Peter Keevash*and*Andrew Treglown for their comments*on*a draft*of*this paper. ...##
###
Connectivity of finite anisotropic random graphs and directed graphs

1986
*
Mathematical proceedings of the Cambridge Philosophical Society (Print)
*

For

doi:10.1017/s0305004100064239
fatcat:wttevbuoc5eclc2ashiz4b5xom
*graphs**on*a finite set*of*vertices with arbitrary probabilities*of*independently occurring edges,*the*reliability is defined as*the*probability that*the**graph*is*connected*,*and**the*redundancy as*the*... Analogous measures*of**connectivity*are defined for*random*finite directed*graphs*with arbitrary probabilities*of*independently occurring directed edges. ... Clearly,*random**graphs*(*digraphs*) are (strongly) P-*connected*if*and*only if*the*matrix P is irreducible. ...##
###
Erdős-Rényi theory for asymmetric digraphs

2018
*
SLUT journal of mathematics
*

We also consider

doi:10.55937/sut/1547570388
fatcat:3r2rgpnqsreclck4rb6ym522y4
*the**random**oriented**graph*RO,*and*make some remarks*on*Aut(RO). ... We introduce*the*concept*of**the*asymmetry number for finite*digraphs*, as a natural generalization*of*that for undirected*graphs*by Erdős*and*Rényi in 1963. ... Acknowledgement We would appreciate Hikoe Enomoto*and*Masatake Hirao for valuable comments*and*suggestions.*The*authors would also like to thank Peter J. Cameron for his careful reading*of*our paper. ...##
###
Page 6764 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
*
Mathematical Reviews
*

In this paper, we show that any CCE-

*orientable**graph*is a CCE-*graph**and*find various families*of**graphs*which are CCE-*orientable**graphs*.” ... Some results concerning anti- Hamiltonian extendable*digraphs**and*anti-Hamiltonian-*connected**digraphs*are presented. ...
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