zbMATH — the first resource for mathematics

Two-line graphs of partial Latin rectangles. (English) Zbl 1397.05027
Garijo, Delia (ed.) et al., Discrete mathematics days 2018. Extended abstracts of the 11th “Jornadas de matemática discreta y algorítmica” (JMDA), Sevilla, Spain, June 27–29, 2018. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 68, 53-58 (2018).
Summary: Two-line graphs of a given partial Latin rectangle are introduced as vertex-and-edge-coloured bipartite graphs that give rise to new autotopism invariants. They reduce the complexity of any currently known method for computing autotopism groups of partial Latin rectangles.
For the entire collection see [Zbl 1392.05001].

MSC:
 05B15 Orthogonal arrays, Latin squares, Room squares 05C76 Graph operations (line graphs, products, etc.) 05C15 Coloring of graphs and hypergraphs
Full Text:
References:
 [1] Artzy, R., A note on the automorphisms of special loops, Riveon Lematematika, 8, 81, (1954), In Hebrew [2] Babai, L., Graph isomorphism in quasipolynomial time, (2016) · Zbl 1376.68058 [3] Babai, L.; Kantor, W. M.; Luks, E. M., Computational complexity and the classification of finite simple groups, (Proc. 24th IEEE FOCS, (1983)), 162-171 [4] Bailey, R. A., Latin squares with highly transitive automorphism groups, J. Aust. Math. Soc., 33, 18-22, (1982) · Zbl 0496.05011 [5] Falcón, R. M., The set of autotopisms of partial Latin squares, Discrete Math., 313, 1150-1161, (2013) · Zbl 1277.05024 [6] R.M. Falcón, D. Kotlar, R.J. Stones, Computing autotopism groups of partial latin rectangles: a pilot study, 2018, submitted for publication. [7] Falcón, R. M.; Stones, R. J., Classifying partial Latin rectangles, Electron. Notes Discrete Math., 49, 765-771, (2015) · Zbl 1346.05021 [8] Falcón, R. M.; Stones, R. J., Partial Latin rectangle graphs and autoparatopism groups of partial Latin rectangles with trivial autotopism groups, Discrete Math., 340, 1242-1260, (2017) · Zbl 1422.05027 [9] R.M. Falcón, R.J. Stones, Enumerating partial latin rectangles, 2018, submitted for publication. · Zbl 1397.05027 [10] Keedwell, A. D., Critical sets and critical partial Latin squares, (Proc. Third China-USA International Conf. on Graph Theory, Combinatorics, Algorithms and Applications, (1994), World Sci. Publishing NJ) [11] Kotlar, D., Computing the autotopy group of a Latin square by cycle structure, Discrete Math., 331, 74-82, (2014) · Zbl 1297.05039 [12] McKay, B. D.; Meynert, A.; Myrvold, W., Small Latin squares, quasigroups, and loops, J. Combin. Des., 15, 98-119, (2007) · Zbl 1112.05018 [13] Schönhardt, E., Über lateinische quadrate und unionen, J. Reine Angew. Math., 163, 183-229, (1930) · JFM 56.0859.01 [14] Stones, D. S., Symmetries of partial Latin squares, European J. Combin., 34, 1092-1107, (2013) · Zbl 1292.05065
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.