7.
An Orthogonal Double Cover (ODC) of the complete graph
Kn by an almost‐hamiltonian cycle is a decomposition of 2
Kn 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
Kn+1 by an almost‐hamiltonian cycle. This yields the existence of an ODC of
Kp+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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