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Cyclic Uniform 2-Factorizations of the Complete Multipartite Graph.

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Title: Cyclic Uniform 2-Factorizations of the Complete Multipartite Graph.
Authors: Pasotti, Anita1 anita.pasotti@unibs.it, Pellegrini, Marco Antonio2 marcoantonio.pellegrini@unicatt.it
Source: Graphs & Combinatorics. Sep2018, Vol. 34 Issue 5, p901-930. 30p.
Subjects: Factorization, Graphic methods, Multiparticle spectrometers, Geometric vertices, Ringel, G.
Abstract: A generalization of the Oberwolfach problem, proposed by Liu (J Comb Des 8:42-49, 2000), asks for a uniform 2-factorization of the complete multipartite graph Km×n. Here we focus our attention on cyclic 2-factorizations, whose 2-factors are disjoint union of cycles all of even length ℓ. In particular, we present a complete solution for the extremal cases ℓ=4 and ℓ=mn. [ABSTRACT FROM AUTHOR]
Copyright of Graphs & Combinatorics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A generalization of the Oberwolfach problem, proposed by Liu (J Comb Des 8:42-49, <xref>2000</xref>), asks for a uniform 2-factorization of the complete multipartite graph Km×n<inline-graphic></inline-graphic>. Here we focus our attention on cyclic 2-factorizations, whose 2-factors are disjoint union of cycles all of even length ℓ<inline-graphic></inline-graphic>. In particular, we present a complete solution for the extremal cases ℓ=4<inline-graphic></inline-graphic> and ℓ=mn<inline-graphic></inline-graphic>. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Graphs & Combinatorics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Graphic methods
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      – SubjectFull: Multiparticle spectrometers
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