Maximum cardinality neighbourly sets in quadrilateral free graphs

K. S. Neethi and Sanjeev Saxena ()
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K. S. Neethi: Indian Institute of Technology
Sanjeev Saxena: Indian Institute of Technology

Journal of Combinatorial Optimization, 2017, vol. 33, issue 2, No 5, 422-444

Abstract: 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.

Keywords: Neighbourly sets; Quadrilateral free graphs; Graphs without $$C_4$$ C 4; Algorithm; Strong edge colouring; Antimatching (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-015-9972-9

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