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Orthogonal Double Covers of Complete Graphs by Caterpillars of Diameter 5

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Abstract

An orthogonal double cover (ODC) of the complete graph K n by a graph G is a collection = {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 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 K n .

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Dr, Duluth, MN, 55812–3000, U.S.A

    Dalibor Froncek

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  1. Dalibor Froncek
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Correspondence to Dalibor Froncek.

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Froncek, D. Orthogonal Double Covers of Complete Graphs by Caterpillars of Diameter 5. Graphs and Combinatorics 23, 145–163 (2007). https://doi.org/10.1007/s00373-007-0693-4

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  • DOI: https://doi.org/10.1007/s00373-007-0693-4

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Mathematics Subject Classification (2000)