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Almost resolvable k ‐cycle systems with k ≡ 2 ( mod 4 )
Author(s) -
Wang L.,
Cao H.
Publication year - 2018
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21608
Subject(s) - mathematics , combinatorics , order (exchange) , economics , finance
Abstract In this paper, we show that if k ≥ 6 and k ≡ 2 ( mod 4 ) , then there exists an almost resolvable k ‐cycle system of order 2 k t + 1 for all t ≥ 1 except possibly for t = 2 and k ≥ 14 . Thus we give a partial solution to an open problem posed by Lindner, Meszka, and Rosa (J. Combin. Des., vol. 17, pp. 404–410, 2009).