Sven Hartmann, Uwe Leck, Volker Leck
A conjecture on orthogonal double covers by paths
Preprint series: Preprints aus dem Fachbereich Mathematik, Universitt Rostock

MSC:

05B30 Other designs, configurations, See also {51E30}

05C70 Factorization, matching, covering and packing

Abstract: An Orthogonal Double Cover (ODC) of the complete graph is a set
of graphs such that every two of them share exactly one edge and
every edge of the complete graph belongs to exactly two of the
graphs. We consider the case when all graphs are paths and
introduce a construction that we conjecture to work in all finite
fields of order $1\bmod 4$.
Keywords: orthogonal double cover, ODC, graph decompositions