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Hamiltonian double latin squares

2003
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Journal of combinatorial theory. Series B (Print)
*

symbols there are four ordered pairs ði; jÞ such that a ij ¼ s h ; a 0 ij ¼ s k : We explore ways of constructing

doi:10.1016/s0095-8956(02)00029-1
fatcat:geeyzeqos5gg3jj4iwrkvioy6y
*Hamiltonian**double**latin**squares*(HLS), symmetric HLS, sets of mutually orthogonal HLS ... A*double**latin**square*of order 2n on symbols s 1 ; y; s n is a 2n 2n matrix A ¼ ða ij Þ in which each a ij is one of the symbols s 1 ; y; s n and each s k occurs twice in each row and twice in each column ... In this paper we study*double**latin**squares*in which the occurrences of each symbol describe a*Hamiltonian*cycle. Such*double**latin**squares*are called*Hamiltonian**double**latin**squares*. ...##
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Page 5164 of Mathematical Reviews Vol. , Issue 2004g
[page]

2004
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Mathematical Reviews
*

The authors give constructions of

*Hamiltonian**double**Latin**squares*, symmetric*Hamiltonian**double**Latin**squares*, and cyclic 05 COMBINATORICS 5164 symmetric*Hamiltonian**double**Latin**squares*. ... A*Hamiltonian**double**Latin**square*, denoted HLS(27), is a*double**Latin**square*in which each o-cycle is a*Hamiltonian*cycle. ...##
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Page 4144 of Mathematical Reviews Vol. , Issue 92h
[page]

1992
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Mathematical Reviews
*

In this paper the author obtains a necessary con- dition and a sufficient condition for constructing

*double*magic*squares*by using orthogonal*Latin**squares*, and constructs the smallest*double*magic*squares*... The so-called*double*magic*squares*are “addition-multiplication magic*squares*”. ...##
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A Parallel Routing Algorithm on Circulant Networks Employing the Hamiltonian Circuit Latin Square
[chapter]

2005
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Lecture Notes in Computer Science
*

For construction of these paths, employing the

doi:10.1007/11577188_22
fatcat:yxnzjhsmt5hrpdpfy36erxvuca
*Hamiltonian*Circuit*Latin**Square*(HCLS) we present O(n 2 ) parallel routing algorithm on circulant networks. ...*Double*-loop and 2-circulant networks are widely used in the design and implementation of local area networks and parallel processing architectures. ... Design of the*Hamiltonian*Circuit*Latin**Square*to the Parallel Routing Algorithm on Circulant Networks Let A and B be any two nodes on G(n; ±s 1 ,±s 2 ,...,±s k ). ...##
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A parallel routing algorithm on circulant networks employing the Hamiltonian circuit latin square☆

2006
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Information Sciences
*

For construction of these paths, employing the

doi:10.1016/j.ins.2005.12.014
fatcat:qfby6ahb45ekhhofxwgqalof5m
*Hamiltonian*Circuit*Latin**Square*(HCLS) we present O(n 2 ) parallel routing algorithm on circulant networks. ...*Double*-loop and 2-circulant networks are widely used in the design and implementation of local area networks and parallel processing architectures. ... Design of the*Hamiltonian*Circuit*Latin**Square*to the Parallel Routing Algorithm on Circulant Networks Let A and B be any two nodes on G(n; ±s 1 ,±s 2 ,...,±s k ). ...##
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Perfect Factorisations of Bipartite Graphs and Latin Squares Without Proper Subrectangles

1999
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Electronic Journal of Combinatorics
*

A

doi:10.37236/1441
fatcat:vqj3dgmx5fal3g55e2s6s5zfiq
*Latin**square*is pan-*Hamiltonian*if every pair of rows forms a single cycle. Such*squares*are related to perfect 1-factorisations of the complete bipartite graph. ... A*square*is atomic if every conjugate is pan-*Hamiltonian*. These*squares*are indivisible in a strong sense – they have no proper subrectangles. ... A*Latin**square*is pan-*Hamiltonian*if and only if it contains no proper subrectangles. In particular every pan-*Hamiltonian**square*is N ∞ . ...##
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Multicolored parallelisms of Hamiltonian cycles

2009
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Discrete Mathematics
*

Fig. 2 is such a

doi:10.1016/j.disc.2008.07.018
fatcat:7xwsp7f22bfybfzikwubregqmq
*latin**square*of order 7. ... For the convenience in the proof of our main result, we shall use a special*latin**square*M = [m i,j ] of order odd n which is a circulant*latin**square*with 1st row (1, n+3 2 , 2, n+5 2 , 3, . . . , n+n ...##
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On the vertices of the d-dimensional Birkhoff polytope
[article]

2012
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arXiv
*
pre-print

More concretely, we show that the number of vertices is at least (L_n)^3/2-o(1), where L_n is the number of order-n

arXiv:1208.4218v1
fatcat:2blffg4eprfxpaoqnw5l6de5ua
*Latin**squares*. ... It is well-known that an order-n*Latin**square*may be viewed as a tristochastic array where every line contains n-1 zeros and a single 1 entry. ... The idea is to use a*Hamiltonian**double**Latin**square*X to define the top n 2 layers of A. ...##
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Orientable Hamilton Cycle Embeddings of Complete Tripartite Graphs I: Latin Square Constructions

2013
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Journal of combinatorial designs (Print)
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A product construction is presented for building pairs of orthogonal

doi:10.1002/jcd.21375
fatcat:rfxf6fla7rfgdpoeawmatfzt74
*latin**squares*such that one member of the pair has a certain*hamiltonian*property. ... In part I, we explore a connection between orthogonal*latin**squares*and embeddings. ... Acknowledgements The first author would like to thank Wendy Myrvold for helpful discussions regarding*latin**squares*. ...##
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Hamiltonian decomposition of K∗n, patterns with distinct differences, and Tuscan squares

1991
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Discrete Mathematics
*

.,

doi:10.1016/0012-365x(90)90235-a
fatcat:jipqsbrajrgrhpy4wlci5dqndu
*Hamiltonian*decomposition of K,*, patterns with distinct differences, and Tuscan*squares*, Discrete Mathematics 91 (1991) 259-276. ... These*Latin**squares*are called Row Complete*Latin**Squares*[8] or Roman*squares*[13] . Most of the known Roman*squares*were obtained by polygonal path constructions [9, 11, 22] . ... A*Latin**square*of order n is an n x n Italian*square*such that each column is a permutation of V,. ...##
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On the Vertices of the d-Dimensional Birkhoff Polytope

2013
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Discrete & Computational Geometry
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The idea is to use a

doi:10.1007/s00454-013-9554-5
fatcat:vx7xa7zuxbarlblyy42opifojm
*Hamiltonian**double**Latin**square*X to define the top n 2 layers of A. ... Let A, B be two order n 2*Latin**squares*and let σ ∈ S n 2 be a cyclic permutation. Then the block matrix X = A B σ(A) B . is an order n*Hamiltonian**double**Latin**square*. ...##
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Page 5762 of Mathematical Reviews Vol. , Issue 95j
[page]

1995
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Mathematical Reviews
*

Preece, How many 7 x 7

*Latin**squares*can be partitioned into Youden*squares*? (343- 352); D. A. Preece and B. J. ... Vowden, Graeco-*Latin**squares*with embedded balanced superimpositions of Youden*squares*(353- 363); Zdenék Ryjaéek and Ingo Schiermeyer, On the independence number in K),,,\-free graphs (365-374); Abdén ...##
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Forthcoming papers

1990
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Discrete Mathematics
*

A well-known conjecture of Thomassen says that every 4-connected line graph is

doi:10.1016/0012-365x(90)90069-t
fatcat:wzbr5q4ikzhxxb4lvuteckukqm
*hamiltonian*. In this paper we prove that every 7-connected line graph is*hamiltonian*-connected. Michael 0. ... The following papers will be published in future issues: Siming Zhan, On*hamiltonian*line graphs and connectivity. ... Lamken, The existence of 3 orthogonal partitioned incomplete*Latin**squares*of type P. ...##
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Page 1848 of Mathematical Reviews Vol. , Issue 82e
[page]

1982
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Mathematical Reviews
*

The author uses the construction of a row complete

*Latin**square*to show that Kj,, can be decomposed into 2m edge-disjoint directed*Hamiltonian*paths. ... A*Latin**square*L is said to be row complete if, for all ordered pairs (u,v) of distinct symbols used in L, there is a row containing u and v as successive elements in the order given. ...##
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Page 850 of Mathematical Reviews Vol. 47, Issue 4
[page]

1974
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Mathematical Reviews
*

Suppose that H is the unique graph that satisfies the “

*Latin**square*graph” characterization but is not a*Latin**square*graph. ... Moon [ibid. 34 (1963), 664- 667; MR 26 #5559] have characterized*Latin**square*graphs. With one exception, a graph is a*Latin**square*graph if and only if it has n? ...
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