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Maximal independent sets in a generalisation of caterpillar graph

Author

Listed:
  • K. S. Neethi

    (Indian Institute of Technology
    Microsoft R&D)

  • Sanjeev Saxena

    (Indian Institute of Technology)

Abstract

A caterpillar graph is a tree which on removal of all its pendant vertices leaves a chordless path. The chordless path is called the backbone of the graph. The edges from the backbone to the pendant vertices are called the hairs of the caterpillar graph. Ortiz and Villanueva (Discret Appl Math 160(3): 259–266, 2012) describe an algorithm, linear in the size of the output, for finding the family of maximal independent sets in a caterpillar graph. In this paper, we propose an algorithm, again linear in the output size, for a generalised version of caterpillar graph, where at each vertex of the backbone, there can be any number of hairs of length one and at most one hair of length two.

Suggested Citation

  • K. S. Neethi & Sanjeev Saxena, 2017. "Maximal independent sets in a generalisation of caterpillar graph," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 326-332, January.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:1:d:10.1007_s10878-015-9960-0
    DOI: 10.1007/s10878-015-9960-0
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