Geodesic
Perfect factorisations of bipartite graphs and Latin squares without proper subrectangles
The electronic journal of combinatorics, Tome 6 (1999)
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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. We give some existence results and a catalogue for small orders. In the process we identify all the perfect 1-factorisations of $K_{n,n}$ for $n\leq 9$, and count the Latin squares of order $9$ without proper subsquares.
DOI : 10.37236/1441
Classification : 05B15, 05C70
Mots-clés : Latin squares, pan-Hamiltonian, perfect 1-factorization, main class 
@article{10_37236_1441,
     author = {I. M. Wanless},
     title = {Perfect factorisations of bipartite graphs and {Latin} squares without proper subrectangles},
     journal = {The electronic journal of combinatorics},
     year = {1999},
     volume = {6},
     doi = {10.37236/1441},
     zbl = {0915.05023},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1441/}
}
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I. M. Wanless. Perfect factorisations of bipartite graphs and Latin squares without proper subrectangles. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1441

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