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Hamiltonian double latin squares
2003
Journal of combinatorial theory. Series B (Print)
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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 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. ...
doi:10.1016/s0095-8956(02)00029-1
fatcat:geeyzeqos5gg3jj4iwrkvioy6y
Page 5164 of Mathematical Reviews Vol. , Issue 2004g
[page]
2004
Mathematical Reviews
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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. ...
Page 4144 of Mathematical Reviews Vol. , Issue 92h
[page]
1992
Mathematical Reviews
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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”. ...
A Parallel Routing Algorithm on Circulant Networks Employing the Hamiltonian Circuit Latin Square
[chapter]
2005
Lecture Notes in Computer Science
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For construction of these paths, employing the 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 ). ...
doi:10.1007/11577188_22
fatcat:yxnzjhsmt5hrpdpfy36erxvuca
A parallel routing algorithm on circulant networks employing the Hamiltonian circuit latin square☆
2006
Information Sciences
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For construction of these paths, employing the 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 ). ...
doi:10.1016/j.ins.2005.12.014
fatcat:qfby6ahb45ekhhofxwgqalof5m
Perfect Factorisations of Bipartite Graphs and Latin Squares Without Proper Subrectangles
1999
Electronic Journal of Combinatorics
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A 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 ∞ . ...
doi:10.37236/1441
fatcat:vqj3dgmx5fal3g55e2s6s5zfiq
Multicolored parallelisms of Hamiltonian cycles
2009
Discrete Mathematics
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Fig. 2 is such a 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 ...
doi:10.1016/j.disc.2008.07.018
fatcat:7xwsp7f22bfybfzikwubregqmq
On the vertices of the d-dimensional Birkhoff polytope
[article]
2012
arXiv
pre-print
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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 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. ...
arXiv:1208.4218v1
fatcat:2blffg4eprfxpaoqnw5l6de5ua
Orientable Hamilton Cycle Embeddings of Complete Tripartite Graphs I: Latin Square Constructions
2013
Journal of combinatorial designs (Print)
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A product construction is presented for building pairs of orthogonal 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. ...
doi:10.1002/jcd.21375
fatcat:rfxf6fla7rfgdpoeawmatfzt74
Hamiltonian decomposition of K∗n, patterns with distinct differences, and Tuscan squares
1991
Discrete Mathematics
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., 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,. ...
doi:10.1016/0012-365x(90)90235-a
fatcat:jipqsbrajrgrhpy4wlci5dqndu
On the Vertices of the d-Dimensional Birkhoff Polytope
2013
Discrete & Computational Geometry
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The idea is to use a 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. ...
doi:10.1007/s00454-013-9554-5
fatcat:vx7xa7zuxbarlblyy42opifojm
Page 5762 of Mathematical Reviews Vol. , Issue 95j
[page]
1995
Mathematical Reviews
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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 ...
Forthcoming papers
1990
Discrete Mathematics
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A well-known conjecture of Thomassen says that every 4-connected line graph is 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. ...
doi:10.1016/0012-365x(90)90069-t
fatcat:wzbr5q4ikzhxxb4lvuteckukqm
Page 1848 of Mathematical Reviews Vol. , Issue 82e
[page]
1982
Mathematical Reviews
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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. ...
Page 850 of Mathematical Reviews Vol. 47, Issue 4
[page]
1974
Mathematical Reviews
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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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