Abstract
A forbidden subgraphs characterization of the class of graphs that arise from bipartite graphs, odd holes, and graphs with no complement of a diamond via repeated substitutions is given. This characterization allows us to solve the vertex packing problem for the graphs in this class.
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References
Berge, C.: Graphs, and Hypergraphs, Amsterdam: North-Holland 1973
Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications London: Macmillian 1976
Chvátal, V., Sbihi, N.: Bull-Free Graphs Are Perfect, Graphs and Combinatorics3, 127–139 (1987)
De Simone, C., Sassano, A.: Stability Number of Bull and Chair Free Graphs, IASI Technical Report R. 258, May 1989 (to appear in Discrete Applied Mathematics)
Garey, M.R., Johnson, D.S., Stockmeyer, L.: Some simplified NP-complete graph problems, Theor. Comput. Sci.1, 237–267 (1976)
Grötschel, M., Lovász, L., and Schrijver, A.: Polynomial Algorithms for Perfect Graphs, in: C. Berge and V. Chvátel, eds., Topics on Perfect Graphs (Annals of Discrete Mathematics21, pp. 325–356) 1984
Hammer, P.L., Mahadev, N.V.R., De, Werra, D.: The Struction Of A Graph: Application To CN-free Graphs, Combinatorica5, 141–147 (1985)
Hsu, W.-L., Ikura, Y., Nemhauser, G.L.: A polynomial Algorithm For Maximum Weighted Vertex Packing On Graphs Without Long Odd Cycles, Math. Programming20, 225–232 (1982)
Lovász, L., Plummer, M.D.: Matching theory. Annals of Discrete Mathematics29, (1986)
Minty, G.J.: On maximal independent sets of vertices in claw-free graphs. J. of Comb. Theory Ser.B28, 284–304 (1980)
Poljak, S.: A note on stable sets and coloring of graphs, Comment. Math. Univ. Carrolin15, 307–309 (1974)
Sbihi, N.: Algorithme de recherche d'un stable de cardinalité maximum dans un graphe sans étoile, Discrete Math.29, 53–76 (1980)
Seinsche, D.: On a property of the class ofn-colourable graphs. J. Comb. Theory Ser.B16, 191–193 (1974)
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De Simone, C. On the vertex packing problem. Graphs and Combinatorics 9, 19–30 (1993). https://doi.org/10.1007/BF01195324
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DOI: https://doi.org/10.1007/BF01195324