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Star-shape, Radon number, and minty graphs

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Literature Cited

  1. 1.

    A. A. Zykov, Theory of Finite Graphs. I [in Russian], Nauka, Novosibirsk (1969).

  2. 2.

    P. Duchet and H. Meyniel, “Ensemble convexes dans les graphes. I. Théorèmes de Helly et de Radon pour graphes et surfaces,” European J. Combin.,4, No. 2, 127–132 (1983).

  3. 3.

    V. G. Boltyanskii and P. S. Soltan, Combinatorial Geometry of Various Classes of Convex Sets [in Russian], Shtiintsa, Kishinev (1978).

  4. 4.

    F. Harary, Graph Theory, Addison-Wesley, Reading (1969).

  5. 5.

    F. W. Levi, “On Helly's theorem and the axioms of convexity,” J. Indian Math. Soc.,15, 65–76 (1951).

  6. 6.

    N. Sbihi, Étude des stables dans les graphes sans étoiles. Thése de docteur. Univ. Sci. et Med., Grenoble (1978).

  7. 7.

    G. J. Minty, “On maximal independent sets of vertices in claw-free graphs,” J. Combin. Theory Ser. B28, No. 3, 284–304 (1980).

  8. 8.

    V. E. Alekseev, “On the influence of local constraints on the complexity of the determination of the independence number of graph,” in: Combinatorial-Algebraic Methods in Applied Mathematics, Gor'kov. Gos. Univ., Gorkii (1984), pp. 3–13.

  9. 9.

    A. C. M. van Rooij and H. S. Wilf, “The interchange graph of a finite graph,” Acta Math. Acad. Sci. Hung.,16, 263–269 (1965).

  10. 10.

    M. A. Krasnosel'skii, “On a criterion for a domain to be star-shaped,” Mat. Sb.,19, (61), 309–310 (1946).

  11. 11.

    J. Borwein, “A proof of the equivalence of Helly's and Krasnoselski's theorems,” Can. Math. Bull.,20, No. 1, 35–37 (1977).

  12. 12.

    V. P. Soltan and O. I. Topalé, “On metric analogues of star-shaped sets,” in: Contemporary Problems of Applied Mathematics and Programming [in Russian], Shtiintsa, Kishinev (1984), pp. 122–128.

  13. 13.

    O. I. Topalé, “Star-shape on graphs,” Mat. Issled., No. 78, 130–133 (1984).

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Additional information

Translated from Kibernetika, No. 2, pp. 1–5, 9, March–April, 1987.

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German, L.F., Topale, O.I. Star-shape, Radon number, and minty graphs. Cybern Syst Anal 23, 147–153 (1987). https://doi.org/10.1007/BF01071768

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Keywords

  • Operating System
  • Artificial Intelligence
  • Radon
  • System Theory
  • Radon Number