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A small embedding for partial even‐cycle systems
Author(s) -
Horak Peter,
Lindner C. C.
Publication year - 1999
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/(sici)1520-6610(1999)7:3<205::aid-jcd4>3.0.co;2-5
Subject(s) - mathematics , combinatorics , embedding , order (exchange) , upper and lower bounds , discrete mathematics , mathematical analysis , computer science , finance , artificial intelligence , economics
Let m = 2 k . We show that for some 0 ≤ ξ <1, a partial directed m ‐cycle system of order n can be embedded in a directed m ‐cycle system of order ( mn )/2 + (2m 2 1) √(8n + 1)/4 + 4 m 3 2 + 4 + 1/2. For fixed m , this is asymptotic in n to ( mn )/2 and so for large n is roughly one‐fourth the best known bound of 2 mn + 1. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 205–215, 1999