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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. ...##
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Infinite Hamiltonian paths in Cayley digraphs

1985
*
Discrete Mathematics
*

In this paper, we give conditions

doi:10.1016/0012-365x(85)90078-0
fatcat:hyjvxtfuc5chbnmuzsq2srldzu
*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*). ...##
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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*...##
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Dihedral Butterfly Digraph and Its Cayley Graph Representation

2008
*
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
*

It is well known that a butterfly

doi:10.1093/ietfec/e91-a.2.613
fatcat:u6j3yj2konhijodmnw3upiu6ry
*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 ...##
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Packing Strong Subgraph in Digraphs
[article]

2021
*
arXiv
*
pre-print

Finally we study the arc-disjoint

arXiv:2110.12783v1
fatcat:kikggvpihrfznkrk2bzfkuambu
*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. ...##
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Spanning Trees: A Survey

2010
*
Graphs and Combinatorics
*

We mainly deal with spanning trees having

doi:10.1007/s00373-010-0973-2
fatcat:y6w7gmq5kfdula4heioxocsn3a
*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. ...##
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Master index of volumes 161–170

1997
*
Discrete Mathematics
*

Yeo,

doi:10.1016/s0012-365x(97)80759-5
fatcat:gk2zgbbx5nbnzbtsvdvo2mkqbi
*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 ...##
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QCSP on Semicomplete Digraphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over semicomplete

doi:10.1007/978-3-662-43948-7_70
fatcat:agbjdcmwvresdoenw2ghkh5tou
*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. ...##
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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. ...##
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Master index of volumes 131–140

1995
*
Discrete Mathematics
*

Allouche Broere,

doi:10.1016/s0012-365x(00)80001-1
fatcat:3p4banfgz5bt3mddvnbajvmyqe
*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 ...##
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Recent Advances on the Hamiltonian Problem: Survey III

2013
*
Graphs and Combinatorics
*

For completeness

doi:10.1007/s00373-013-1377-x
fatcat:mysq2guixrcblm2haaqfu24t6u
*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. ...##
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Trees, Forests, and Stationary States of Quantum Lindblad Systems
[article]

2018
*
arXiv
*
pre-print

We show that they can be characterized in terms

arXiv:1810.11144v1
fatcat:qnao6kh2lnhs5g2kdpf2d5nd24
*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 ...##
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Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking

2020
*
SciPost Physics
*

We relate these to each other in the context

doi:10.21468/scipostphys.8.2.022
fatcat:wfkl3krikzgtdnuwlmuwptifqi
*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. ...##
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Shortcutting directed and undirected networks with a degree constraint

2017
*
Discrete Applied Mathematics
*

Finally, we prove bounds for special classes

doi:10.1016/j.dam.2016.12.016
fatcat:f2d2rshbdbenvg673txg3755vm
*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*. ...##
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Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking
[article]

2019
*
arXiv
*
pre-print

We relate these to each other in the context

arXiv:1811.12109v3
fatcat:zwkwgfblznemzdufwsufaqlfky
*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. ...
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