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Effective subdirect decompositions of regular semigroups

✍ Scribed by Miroslav Ćirić; Žarko Popović; Stojan Bogdanović

Publisher: Springer
Year: 2008
Tongue: English
Weight: 456 KB
Volume: 77
Category: Article
ISSN: 0037-1912
DOI: 10.1007/s00233-008-9114-0

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## Abstract Kotzig asked in 1979 what are necessary and sufficient conditions for a __d__‐regular simple graph to admit a decomposition into paths of length __d__ for odd __d__>3. For cubic graphs, the existence of a 1‐factor is both necessary and sufficient. Even more, each 1‐factor is extendable