Uwe Leck, Volker Leck
Orthogonal Double covers of complete graphs by trees of short diameter
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

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

05B15 Orthogonal arrays, Latin squares, Room squares

Abstract: A collection P of n spanning subgraphs of the complete graph K_n is an
orthogonal double cover (ODC) of K_n if every edge of K_n belongs to
exactly two members of P, and if every two members of P share exactly
one edge. P is an ODC of K_n by some graph G if all graphs in P are
isomorphic to G. Gronau, Mullin, and Rosa conjecture, that every tree
except the path with 4 vertices admits ODC of the fitting K_n. They
proved, this to be true for trees of diameter 3. In this paper, we
show the correctness of their conjecture for some classes of trees
of diameter 4.
Keywords: ortogonal double cover, 2-factorization