Abstract

An orthogonal double cover (ODC) of the complete graph Kn by a graph G is a collection ** = {Gi|i = 1,2, . . . ,n} of spanning subgraphs of Kn, all isomorphic to G, with the property that every edge of Kn belongs to exactly two members of ** and any two distinct members of ** share exactly one edge. A caterpillar of diameter five is a tree arising from a path with six vertices by attaching pendant vertices to some or each of its vertices of degree two. We show that for any caterpillar of diameter five there exists an ODC of the complete graph Kn.

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