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Maximum cardinality neighbourly sets in quadrilateral free graphs

Author

Listed:
  • K. S. Neethi

    (Indian Institute of Technology
    Microsoft R & D)

  • Sanjeev Saxena

    (Indian Institute of Technology)

Abstract

Neighbourly set of a graph is a subset of edges which either share an end point or are joined by an edge of that graph. The maximum cardinality neighbourly set problem is known to be NP-complete for general graphs. Mahdian (Discret Appl Math 118:239–248, 2002) proved that it is in polynomial time for quadrilateral-free graphs and proposed an $$O(n^{11})$$ O ( n 11 ) algorithm for the same, here n is the number of vertices in the graph, (along with a note that by a straightforward but lengthy argument it can be proved to be solvable in $$O(n^5)$$ O ( n 5 ) running time). In this paper we propose an $$O(n^2)$$ O ( n 2 ) time algorithm for finding a maximum cardinality neighbourly set in a quadrilateral-free graph.

Suggested Citation

  • K. S. Neethi & Sanjeev Saxena, 2017. "Maximum cardinality neighbourly sets in quadrilateral free graphs," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 422-444, February.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:2:d:10.1007_s10878-015-9972-9
    DOI: 10.1007/s10878-015-9972-9
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