Hertz, Alainde Werra, Dominique2010-11-302010-11-302010-11-30200910.1007/s00373-010-0886-0https://infoscience.epfl.ch/handle/20.500.14299/59451WOS:000274852300005A 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.Stable setMagnetGraph transformationEven pairP-4-free pairWeakly Triangulated Graphstext::journal::journal article::research article