By Jacques Lesourne (auth.), Denis Bouyssou, Eric Jacquet-Lagrèze, Patrice Perny, Roman Słowiński, Daniel Vanderpooten, Philippe Vincke (eds.)
Aiding judgements With a number of standards: Essays in Honor of BernardRoy is geared up round large subject matters:
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Extra info for Aiding Decisions with Multiple Criteria: Essays in Honor of Bernard Roy
2:71-85. Rote, G. (1985). A systolic array algorithm for the algebraic path problem (shortest paths; matrix inversion). Computing 34:191-219. Roy, B. (1958). Sur quelques proprietes des graphes fortement connexes. C. R. Acad. Sci. Paris 247:399-401. 42 AIDING DECISIONS WITH MULTIPLE CRITERIA Roy, B. (1959a). Contribution de la theorie des graphes al'etude de certains problemes lineaires. C. R. Acad. Sci. Paris 248:2437-2439. Roy, B. (1959b). Transitivite et connexite. C. R. Acad. Sci. Paris 249:216-218.
Res. Develop. 16:412-414. C. (1967). Revised matrix algorithms for shortest paths. SIAM J. Appl. Math. 15:207-218. J. (1976). The structure of Sperner k-families. J. Combin. Theory A 20:41-68. T. (1989). An algorithm for transitive reduction of an acyclic graph. Sci. Comput. Programming 12:151-155. , and Larman, D. (1979). Use of Floyd's algorithm to find shortest restricted paths. Ann. of Discrete Math. 4:237-249. W. (1967). The extension of the cascade algorithm to large graphs. Manag. Sci. 14:29-33.
A k-coloring of G. (b) For any vertex x in 8 h+ 1 , the chromatic number of the subgraph Gh(x) of G induced by 8 1 ,82 , ... , 8 h and x satisfies X(Gh(x)) = h+l. Fig. 4 (a) shows a 4-coloring of a graph G with X(G) = 4, in Fig. 2 (b) an orientation without circuits is given (it is derived in fact from the coloring in Fig. 2 (a)) with a 4-coloring having Property (a) of Theorem 9. Notice that it does not satisfy Property (b) since the subgraph generated by 81, 8 2 and x is 2-colorable. The proof technique of B.
Aiding Decisions with Multiple Criteria: Essays in Honor of Bernard Roy by Jacques Lesourne (auth.), Denis Bouyssou, Eric Jacquet-Lagrèze, Patrice Perny, Roman Słowiński, Daniel Vanderpooten, Philippe Vincke (eds.)