Logical Aspects of Combinatorial Duality
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 251-256

Voir la notice de l'article provenant de la source Cambridge University Press

D. R. Woodall has introduced closely-related notions of Menger and König duals which can be applied to a broad range of combinatorial contexts. The present paper considers these two notions for finite ground sets in terms of syntactic duality principles. Specific graph-theoretic interpretations are cited.
DOI : 10.4153/CMB-1984-037-8
Mots-clés : 03B10, 05-00, 05B35, 05C99
McKee, T. A. Logical Aspects of Combinatorial Duality. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 251-256. doi: 10.4153/CMB-1984-037-8
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[1] 1. Edmonds, J. and Fulkerson, D. R., Bottleneck extrema, J. Combinatorial Theory 8 (1970), 299–306. Google Scholar

[2] 2. Harary, F., Graph theory, Addison-Wesley, Reading, MA, 1969. Google Scholar

[3] 3. Keisler, H. J., Fundamentals of model theory, in Barwise, J., ed., Handbook of mathematical logic (North-Holland, Amsterdam, 1977), 47–103. Google Scholar

[4] 4. McKee, T. A., A quantifier for matroid duality, Discrete Math. 34 (1981), 315–318. Google Scholar

[5] 5. McKee, T. A., Logical and matroidal duality in combinatorial linear programming (in Proc. 11th Southeastern Conf. Combinatorics, Graph Theory & Computing), Congressus Numerantium 29 (1980), 667–672. Google Scholar

[6] 6. McKee, T. A., Prime implicant quantifiers for matroids, graphs, and switching networks, Utilitas Math. 24 (1983), 155–163. Google Scholar

[7] 7. McKee, T. A., Duality principles for binary matroids and graphs, Discrete Math., 43 (1983), 215–222. Google Scholar

[8] 8. McKee, T. A., Series-parallel graphs: a logical approach, J. Graph Theory, 7 (1983), 177–181. Google Scholar

[9] 9. Vandewalle, J. and Chua, L. U., The colored branch theorem and its applications in circuit theory, IEEE Trans. Circuit Theory 27 (1980), 816–825. Google Scholar

[10] 10. Woodall, D. R., Menger and Konig systems, in Y. Alavi and Lick, D. R., eds, Theory and applications of graphs, Lecture Notes in Mathematics 642 (Springer-Verlag, Berlin, 1978), 620–635. Google Scholar

[11] 11. Woodall, D. R., Minimax theorems in graph theory, in Beineke, L. W. and Wilson, R. J., eds, Selected topics in graph theory (Academic Press, New York, 1978), 237–269. Google Scholar

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