A Magnetic Procedure for the Stability Number

A magnet is a pair u, v of adjacent vertices such that the proper neighbours of u are completely linked to the proper neighbours of v. It has been shown that one can reduce the graph by removing the two vertices u, v of a magnet and introducing a new vertex linked to all common neighbours of u and v without changing the stability number. We prove that all graphs containing no chordless cycle C-k (k >= 5) and none of eleven forbidden subgraphs can be reduced to a stable set by repeated use of magnets. For such graphs a polynomial algorithm is given to determine the stability number.

Published in:
Graphs And Combinatorics, 25, 707-716

 Record created 2010-11-30, last modified 2018-03-17

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