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research article
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.
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Type
research article
Web of Science ID
WOS:000274852300005
Authors
Publication date
2009
Published in
Volume
25
Start page
707
End page
716
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
November 30, 2010