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On the construction of odd cycle systems
Author(s) -
Hoffman D. G.,
Lindner C. C.,
Rodger C. A.
Publication year - 1989
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190130405
Subject(s) - mathematics , combinatorics , order (exchange) , existential quantification , discrete mathematics , economics , finance
Three obvious necessary conditions for the existence of a k ‐cycle system of order n are that if n > 1 then n ⩾ k, n is odd, and 2 k divides n ( n − 1). We show that if these necessary conditions are sufficient for all n satisfying k ⩽ n < 3 k then they are sufficient for all n. In particular, there exists a 15‐cycle system of order n if and only if n ≡ 1, 15, 21, or 25 (mod 30), and there exists a 21‐cycle system of order n if and only if n ≡ 1, 7, 15, or 21 (mod 42), n ≠ 7. 15.