A Class of 2-Colorable Orthogonal Double Covers of Complete Graphs by Hamiltonian Paths |
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Authors: | Uwe Leck |
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Institution: | 1.Universit?t Rostock, Fachbereich Mathematik, 18051 Rostock, Germany e-mail: uwe.leck@mathematik.uni-rostock.de,DE |
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Abstract: | K
n
by a graph G is a collection ? of n spanning subgraphs of K
n
, all isomorphic to G, such that any two members of ? share exactly one edge and every edge of K
n
is contained in exactly two members of ?. In the 1980's Hering posed the problem to decide the existence of an ODC for the
case that G is an almost-hamiltonian cycle, i.e. a cycle of length n−1. It is known that the existence of an ODC of K
n
by a hamiltonian path implies the existence of ODCs of K
4n
and K
16n
, respectively, by almost-hamiltonian cycles. Horton and Nonay introduced 2-colorable ODCs and showed: If for n≥3 and a prime power q≥5 there are an ODC of K
n
by a hamiltonian path and a 2-colorable ODC of K
q
by a hamiltonian path, then there is an ODC of K
qn
by a hamiltonian path. We construct 2-colorable ODCs of K
n
and K
2n
, respectively, by hamiltonian paths for all odd square numbers n≥9.
Received: January 27, 2000 |
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Keywords: | , ,Orthogonal double cover, Graph decompositions, Self-orthogonal decompositions, Self-orthogonal 2-sequencings, Hering's,,,,,problem |
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