On Orthogonal Double Covers by Hamilton Paths
Preprints aus dem Fachbereich Mathematik, Universitt Rostock
Abstract: An Orthogonal Double Cover (ODC) of the complete graph $K_n$ is a
- 05C70 Factorization, matching, covering and packing
- 05C45 Eulerian and Hamiltonian graphs
set of isomorphic graphs such that two
of them share exactly one edge and all together cover the complete graph
twice. In the case of
paths the problem is also known as self-orthogonal Hamilton path
decomposition of $2K_n$. Solutions generated by a group correspond to
self-orthogonal $2$-sequencings of this group.
We present small solutions which can be applied to
a well-known recursive construction. This gives new classes of such ODCs.
Keywords: orthogonal double cover, Hamilton path