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Orthogonal double covers by super-extendable cycles

✍ Scribed by Christian Bey; Sven Hartmann; Uwe Leck; Volker Leck

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 115 KB
Volume: 10
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.10011

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✦ Synopsis

Abstract

An Orthogonal Double Cover (ODC) of the complete graph K~n~ by an almost‐hamiltonian cycle is a decomposition of 2__K__~n~ into cycles of length n−1 such that the intersection of any two of them is exactly one edge. We introduce a new class of such decompositions. If n is a prime, the special structure of such a decomposition allows to expand it to an ODC of K~n+1~ by an almost‐hamiltonian cycle. This yields the existence of an ODC of K~p+1~ by an almost‐hamiltonian cycle for primes p of order 3 mod 4 and its eventual existence for arbitrary primes p. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 283–293, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10011

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