The struction of a graph: Application toCN-free graphs

Abstract

We consider the class of graphs characterized by the forbidden subgraphsC andN:C is the claw (unique graph with degree sequence (3, 1, 1, 1)) andN the net (unique graph with degree sequence (3, 3, 3, 1, 1, 1)). For this class of graphs (calledCN-free) an algorithm is described for determining the stability numberα(G). It is based on a construction associating with anyCN-free graphG anotherCN-free graphG′ such thatα(G′)=α(G)−1. Such a construction reducing the stability number is called a struction.

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This work was completed while this author was visiting the Dept. of Combinatories and Optimization at the University of Waterloo, Ontario.

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Hammer, P.L., Mahadev, N.V.R. & de Werra, D. The struction of a graph: Application toCN-free graphs. Combinatorica 5, 141–147 (1985). https://doi.org/10.1007/BF02579377

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AMS subject classification (1980)

  • 05 C 99
  • 68 E 10