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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

Guy Melançon, Fabrice Philippe
2004 Information Processing Letters  
This algorithm is an extension 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 .  ... 
doi:10.1016/j.ipl.2003.06.002 fatcat:vlxbc4ppu5ge5cvozdmlfbppfq

Hochschild homology, and a persistent approach via connectivity digraphs [article]

Luigi Caputi, Henri Riihimäki
2022 arXiv   pre-print
To extend them to higher degrees, we introduce 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  ... 
arXiv:2204.00462v1 fatcat:5wzkv7v6kbfjpjxiuxy4lbwu6a

Generating connected acyclic digraphs uniformly at random [article]

Guy Melancon, Fabrice Philippe
2004 arXiv   pre-print
This algorithm is an extension 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  ... 
arXiv:cs/0403040v1 fatcat:73cdb2sutrhk3ooepnsq24vutq

Orbits of rotor-router operation and stationary distribution of random walks on directed graphs

Trung Van Pham
2015 Advances in Applied Mathematics  
In this paper we prove that all orbits 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.  ... 
doi:10.1016/j.aam.2015.06.006 fatcat:bcz5dfs745eyflt67ebegz7key

The birth of the contradictory component in random 2-SAT [article]

Sergey Dovgal
2019 arXiv   pre-print
This follows from 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.  ... 
arXiv:1904.10266v1 fatcat:4inbubamozcizamt65w5qyp5jq

Maximum directed cuts in acyclic digraphs

Noga Alon, Béla Bollobás, András Gyárfás, Jenő Lehel, Alex Scott
2007 Journal of Graph Theory  
We investigate 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.  ... 
doi:10.1002/jgt.20215 fatcat:yk4lc6wug5drfm24new6zf5rfa

Sizing the length of complex networks [article]

Gorka Zamora-López, Romain Brasselet
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.  ... 
arXiv:1810.12825v1 fatcat:sdguphjwsjci7f7ivdzfactz4u

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]

M. Drew Lamar
2009 arXiv   pre-print
It has been shown in 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.  ... 
arXiv:0912.3834v1 fatcat:btygwyiiljdwdemtxh4idkcl4a

Extremal results on feedback arc sets in digraphs [article]

Jacob Fox, Zoe Himwich, Nitya Mani
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.  ... 
arXiv:2204.01938v2 fatcat:ob2rf3zovvbzjkmcffrlhtzysm

A survey on Hamilton cycles in directed graphs [article]

Daniela Kühn, Deryk Osthus
2010 arXiv   pre-print
We survey some recent results 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.  ... 
arXiv:1006.0590v1 fatcat:vayfrvmx2vba7fnbrhoriu2dxq

Connectivity of finite anisotropic random graphs and directed graphs

Joel E. Cohen
1986 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
For 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.  ... 
doi:10.1017/s0305004100064239 fatcat:wttevbuoc5eclc2ashiz4b5xom

Erdős-Rényi theory for asymmetric digraphs

Shohei Satake, Masanori Sawa, Masakazu Jimbo
2018 SLUT journal of mathematics  
We also consider 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.  ... 
doi:10.55937/sut/1547570388 fatcat:3r2rgpnqsreclck4rb6ym522y4

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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