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  • All lobsters with perfect matchings are graceful
  • Morgan, David
  • Graceful labelling
    Lobster
    Perfect matching
  • report
  • English
  • Technical report TR05-01. Given a tree T consider one of its longest paths P_T. We define T to be m-distant if all of its vertices are a distance at most m from P_T. We will show that any 3-distant tree satisfying both of the following properties is graceful. The tree has a perfect matching. The tree can be constructed by attaching paths of length two to the vertices of a 1-distant tree (caterpillar); these attachments are made by identifying an end vertex of each path of length two with a vertex of the 1-distant tree.