arXiv Open Access 2018

Quasi-transversal in Latin Squares

Adel P. Kazemi Behnaz Pahlavsay

Lihat Sumber

Abstrak

In this paper, we first present the relation between a transversal in a Latin square with some concepts in its Latin square graph, and give an equivalent condition for a Latin square has an orthogonal mate. The most famous open problem involving Combinatorics is to find maximum number of disjoint transversals in a Latin square. So finding some family of decomposable Latin squares into disjoint transversals is our next aim. In the next section, we give an equivalent statement of a conjecture which has been attributed to Brualdi, Stein and Ryser by the concept of quasi-transversal. Finally, we prove the truth of the Rodney's conjecture for a family of graphs.

Topik & Kata Kunci

math.CO

Penulis (2)

Adel P. Kazemi

Behnaz Pahlavsay

Format Sitasi

APA MLA BibTeX

Kazemi, A.P., Pahlavsay, B. (2018). Quasi-transversal in Latin Squares. https://arxiv.org/abs/1808.05213

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2018
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓