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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Universal cycles for minimum coverings of pairs by triples, with application to 2-radius sequences


Authors: Yeow Meng Chee, San Ling, Yin Tan and Xiande Zhang
Journal: Math. Comp. 81 (2012), 585-603
MSC (2010): Primary 05B05, 05B07, 05B40; Secondary 05C38, 68R05
Published electronically: June 21, 2011
MathSciNet review: 2833510
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Abstract: A new ordering, extending the notion of universal cycles of Chung et al. (1992), is proposed for the blocks of $ k$-uniform set systems. Existence of minimum coverings of pairs by triples that possess such an ordering is established for all orders. The application to the construction of short 2-radius sequences is given, along with some new 2-radius sequences found through a computer search.


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Additional Information

Yeow Meng Chee
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Email: ymchee@ntu.edu.sg

San Ling
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Email: lingsan@ntu.edu.sg

Yin Tan
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Email: tanyin@ntu.edu.sg

Xiande Zhang
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Email: ziandezhang@ntu.edu.sg

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02473-7
PII: S 0025-5718(2011)02473-7
Keywords: Alternating Hamiltonian cycle, block intersection graph, group divisible design, minimum covering, sequence of radius two, Steiner triple system, universal cycle
Received by editor(s): September 20, 2009
Received by editor(s) in revised form: August 6, 2010
Published electronically: June 21, 2011
Additional Notes: This research was supported in part by the National Research Foundation of Singapore under Research Grant NRF-CRP2-2007-03 and by the Nanyang Technological University under Research Grant M58110040.
Article copyright: © Copyright 2011 American Mathematical Society