Orthogonal Double Covers by Super-Extendable Cycles
نویسندگان
چکیده
An Orthogonal Double Cover (ODC) of the complete graph Kn by an almosthamiltonian cycle is a decomposition of 2Kn 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 Knþ1 by an almost-hamiltonian cycle. This yields the existence of an ODC of Kpþ1 by an almosthamiltonian cycle for primes p of order 3mod 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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