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Page 61 of Mathematical Reviews Vol. , Issue 90A [page]

1990 Mathematical Reviews  
{x;, yj} has three internally disjoint paths between x3_; and y3_;, and T \ {x3_;, y3-;} has two internally disjoint paths between x; and y; for i = 1 or 2, then T has a pair of disjoint paths between  ...  Depending on p, there could be 256 dif- ferent products of graphs. The author investigates the chromatic number x of some of those.  ... 

Infinite Hamiltonian paths in Cayley digraphs

Irwin L Jungreis
1985 Discrete Mathematics  
In this paper, we give conditions on S and H for the existence of one-and two-way infinite Hamiltonian paths in Cay(S:H). Two of our results can be summarized as follows.  ...  Second, we show that any Cayley digraph of a countable locally finite group has both one-and two-way infinite Hamiltonian paths.  ...  Therefore I is normal in (ILl{s})= H. Of course the portion of P in I is a Hamiltonian path in Cay(T).  ... 
doi:10.1016/0012-365x(85)90078-0 fatcat:hyjvxtfuc5chbnmuzsq2srldzu

Page 213 of Mathematical Reviews Vol. 34, Issue 2 [page]

1967 Mathematical Reviews  
Then : (i) py 2 — 1; (ii) the number of strongly connected subgraphs of G with a cyclomatic number ¢ € {1, 2, ---, v} is 2v—t+1; (iii) if deleting of any edge from G causes G to lose the strong connectedness  ...  Two theorems are given which characterize pseudo- symmetric and symmetric oriented graphs in terms of symmetry properties of two integral-valued functions defined on the space of cartesian products of  ... 

Dihedral Butterfly Digraph and Its Cayley Graph Representation

H. ONISHI, Y. TANAKA, Y. SHIBATA
2008 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
It is well known that a butterfly digraph can be represented as a Cayley graph on the wreath product of two cyclic groups [1] .  ...  We call this digraph the dihedral butterfly digraph and study its properties. Furthermore, we show that this digraph can be represented as a Cayley graph.  ...  Acknowledgements This research has been partly supported by a Grant-in-Aid for Scientific Research (c) (2) (No.16500006) from the Japan Society for the Promotion of Science. The authors  ... 
doi:10.1093/ietfec/e91-a.2.613 fatcat:u6j3yj2konhijodmnw3upiu6ry

Packing Strong Subgraph in Digraphs [article]

Yuefang Sun, Gregory Gutin, Xiaoyan Zhang
2021 arXiv   pre-print
Finally we study the arc-disjoint strong subgraph packing problem restricted to digraph compositions and obtain some algorithmic results by utilizing the structural properties.  ...  In this paper, we study two types of strong subgraph packing problems in digraphs, including internally disjoint strong subgraph packing problem and arc-disjoint strong subgraph packing problem.  ...  This work was supported by Zhejiang Provincial Natural Science Foundation of China (No. LY20A010013), National Natural Science Foundation of China (Nos.11871280 and 11971349) and Qing Lan Project.  ... 
arXiv:2110.12783v1 fatcat:kikggvpihrfznkrk2bzfkuambu

Spanning Trees: A Survey

Kenta Ozeki, Tomoki Yamashita
2010 Graphs and Combinatorics  
We mainly deal with spanning trees having some particular properties concerning a hamiltonian properties, for example, spanning trees with bounded degree, with bounded number of leaves, or with bounded  ...  Moreover we also study spanning trees with some other properties, motivated from optimization aspects or application for some problems.  ...  Acknowledgements The authors would like to thank the referees for their helpful comments and corrections.  ... 
doi:10.1007/s00373-010-0973-2 fatcat:y6w7gmq5kfdula4heioxocsn3a

Master index of volumes 161–170

1997 Discrete Mathematics  
Yeo, On k-strong and k-cyclic digraphs Bang-Jensen, 1., G. Gutin and 1. Huang, A sufficient condition for a semicomplete multipartite digraph to be Hamiltonian Bang-Jensen, J., Y. Guo, G.  ...  ., Some recent problems and results in graph theory 164 (1997) 81-85 Erdos, P.L., Splitting property in infinite posets (Note) 163 (1997) 251-256 Erdos, P., Some old and new problems in various  ... 
doi:10.1016/s0012-365x(97)80759-5 fatcat:gk2zgbbx5nbnzbtsvdvo2mkqbi

QCSP on Semicomplete Digraphs [chapter]

Petar Dapić, Petar Marković, Barnaby Martin
2014 Lecture Notes in Computer Science  
We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over semicomplete digraphs.  ...  The largest part of our work is the algebraic classification of precisely which semicompletes enjoy only essentially unary polymorphisms, which is combinatorially interesting in its own right.  ...  a 1 : [a i , a j ] is the set of all vertices that are traversed by shortest path starting at a i , ending at a j and which uses only the directed edges of the Hamiltonian cycle.  ... 
doi:10.1007/978-3-662-43948-7_70 fatcat:agbjdcmwvresdoenw2ghkh5tou

Page 605 of Mathematical Reviews Vol. 50, Issue 3 [page]

1975 Mathematical Reviews  
In this article the author gives the numbers of generalized rooted trees with n vertices and k roots, and with some additional properties.  ...  Kuz’menko, Maximum genus of the Cartesian, the strong Cartesian and the lexicographic product of two graphs (pp. 211-223); M. O. Ostroverhii, Maxi- mum genus of derived graphs (pp. 224-233); M. P.  ... 

Master index of volumes 131–140

1995 Discrete Mathematics  
Allouche Broere, I., J.H. Hattingh, M.A. Henning and A.A. McRae, Dakic, T. and T. Pisanski, On the genus of the tensor product of graphs where one factor is a regular graph Dale, K. and I.  ...  Hochberg McDougal, K., On asymmetric (0, I)-matrices with given row and column sum vectors (Note) Michalak, D., The binding numbers of some Cartesian products of graphs (Note) 15 163-171  ... 
doi:10.1016/s0012-365x(00)80001-1 fatcat:3p4banfgz5bt3mddvnbajvmyqe

Recent Advances on the Hamiltonian Problem: Survey III

Ronald J. Gould
2013 Graphs and Combinatorics  
For completeness of the presentation of both particular questions and the general area, it also contains some material on closely related topics such as traceable, pancyclic and Hamiltonian connected graphs  ...  Theorem 131 [19] Let b ≤ 3/2 and let G be a 2-connected graph on n ≥ 3 vertices such that bind(G) ≥ b and δ(G) ≥ 2−b 3−b n. Then G is pancyclic.  ...  For some properties like being Hamiltonian, removing all edges incident to a vertex of minimum degree destroys the property and thus, yields a trivial upper bound on the global resilience.  ... 
doi:10.1007/s00373-013-1377-x fatcat:mysq2guixrcblm2haaqfu24t6u

Trees, Forests, and Stationary States of Quantum Lindblad Systems [article]

Patrick Rooney, Anthony M. Bloch, Chitra Rangan
2018 arXiv   pre-print
We show that they can be characterized in terms of trees and forests on a directed graph with edge weights that depend on the Lindblad operators and the eigenbasis of the density operator.  ...  In most cases, every asymptotic end-state must be a linear combination thereof, but we prove necessary and sufficient conditions under which symmetry in the Lindblad and Hamiltonian operators hide other  ...  ACKNOWLEDGMENTS The work of P. Rooney  ... 
arXiv:1810.11144v1 fatcat:qnao6kh2lnhs5g2kdpf2d5nd24

Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking

Christiaan J. F. van de Ven, Gerrit C. Groenenboom, Robin Reuvers, Klaas Landsman
2020 SciPost Physics  
We relate these to each other in the context of the Curie–Weiss model, establishing a remarkable relationship between this model (for finite NN) and a discretized Schrödinger operator with double well  ...  Spontaneous symmetry breaking (ssb) is mathematically tied to some limit, but must physically occur, approximately, before the limit.  ...  We are also indebted to Aron Beekman for references on SSB in finite quantum systems.  ... 
doi:10.21468/scipostphys.8.2.022 fatcat:wfkl3krikzgtdnuwlmuwptifqi

Shortcutting directed and undirected networks with a degree constraint

Richard B. Tan, Erik Jan van Leeuwen, Jan van Leeuwen
2017 Discrete Applied Mathematics  
Finally, we prove bounds for special classes of graphs, including e.g. graphs with Hamiltonian cycles or paths.  ...  Improving on a result of Bokhari and Raza we show that, for any δ ≥ 1, every undirected graph G can be shortcut in linear time to a diameter of at most O(log 1+δ n) by the addition of no more than O(n/  ...  By strong connectedness, each segment [u i , v i ] is fully contained in its C i .  ... 
doi:10.1016/j.dam.2016.12.016 fatcat:f2d2rshbdbenvg673txg3755vm

Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking [article]

C. J. F. van de Ven, G. C. Groenenboom, R. Reuvers, N. P. Landsman
2019 arXiv   pre-print
We relate these to each other in the context of the Curie-Weiss model, establishing a remarkable relationship between this model (for finite N) and a discretized Schroedinger operator with double well  ...  Spontaneous symmetry breaking (SSB) is mathematically tied to some limit, but must physically occur, approximately, before the limit.  ...  The following result links irreducibility of a non-negative matrix to strongly connectedness of its corresponding digraph. The proof is easy and therefore omitted. Lemma A.2.  ... 
arXiv:1811.12109v3 fatcat:zwkwgfblznemzdufwsufaqlfky
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