论文信息 - The struction of a graph: Application toCN-free graphs

The struction of a graph: Application toCN-free graphs

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.

[1] George J. Minty,et al. On maximal independent sets of vertices in claw-free graphs , 1980, J. Comb. Theory, Ser. B.

[2] M. Golumbic. CHAPTER 3 – Perfect Graphs , 1980 .

[3] Najiba Sbihi,et al. Algorithme de recherche d'un stable de cardinalite maximum dans un graphe sans etoile , 1980, Discret. Math..

[4] D. R. Lick,et al. The Theory and Applications of Graphs. , 1983 .

[5] P. Hammer,et al. Pseudo-Boolean functions and stability of graphs , 1984 .

[6] M. Golumbic. Algorithmic graph theory and perfect graphs , 1980 .

[7] Peter L. Hammer,et al. Stability in CAN-free graphs , 1985, J. Comb. Theory, Ser. B.