An orthogonal double cover (ODC) of the complete graph K_n by a graph G is a collection G = {G_i|i = 1, 2,..., n} of spanning subgraphs of K_n, all isomorphic to G, with the property that every edge of K_n belongs to exactly two members of G and any two distinct members of G share exactly one edge. A lobster of diameter four is a tree arising from a star K_(1, r), r ≥ 2, by attaching any number of pendant vertices to each of its vertices of degree one. We show that for each K_(1, r) there exists an ODC of K_n by all lobsters of diameter four arising from K_(1, r) except for possibly finitely many.
展开▼
机译：通过图G的完整图K_N的正交双覆盖（ODC）是K_N，所有相像到G的跨越跨越子图的集合G = {g_i | i = 1,2，...，n} K_N的每个边缘都属于G的两个成员，以及G的任何两个不同成员分享到完全的一个边缘。直径四的龙虾是由星形K_（1，R），R≥2引起的树，通过将任意数量的吊坠顶点连接到一个程度的每个顶点。我们表明，对于每个k_（1，r），除了可能有限的k_（1，r）外，所有直径四个直径四个龙虾都存在k_n的ODC。
展开▼
