Orthogonal Double Covers of Complete Graphs by Trees

Gronau, Mullin, and Rosa conjectured that for every tree T with n vertices except for P4 there exists an ODC of Kn by T . They also proved the conjecture for all caterpillars of diameter 3. Later, Leck and Leck proved it for all caterpillars of diameter 4 and all trees with up to 14 vertices. We prove the conjecture for all carerpillars of diameter 5 and order n ≥ 24; for orders 15 ≤ n ≤ 23 we prove it with several exceptions, which we believe are only temporary. The method we use is a common generalization of methods developed for ODCs by Gronau, Mullin, and Rosa and by Leck and Leck and for complete graph factorizations by Tereza Kovarova.