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.
Pasotti, A., Pellegrini, M. A., Cyclic Uniform 2-Factorizations of the Complete Multipartite Graph, <<GRAPHS AND COMBINATORICS>>, 2018; 34 (5): 901-930. [doi:10.1007/s00373-018-1920-x] [http://hdl.handle.net/10807/125384]
Cyclic Uniform 2-Factorizations of the Complete Multipartite Graph
Pasotti, AnitaPrimo
;Pellegrini, Marco Antonio
Secondo
2018
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.
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