Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T09:35:15.533Z Has data issue: false hasContentIssue false
  • English
  • Français

Logical Aspects of Combinatorial Duality

Published online by Cambridge University Press:  20 November 2018

T. A. McKee
T. A. McKee*
Affiliation:
Wright State UniversityDayton, Ohio
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

03B1005-0005B3505C99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 251 - 256
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Edmonds, J. and Fulkerson, D. R., Bottleneck extrema, J. Combinatorial Theory 8 (1970), 299–306.Google Scholar
2. Harary, F., Graph theory, Addison-Wesley, Reading, MA, 1969.Google Scholar
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. McKee, T. A., A quantifier for matroid duality, Discrete Math. 34 (1981), 315–318.Google Scholar
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. McKee, T. A., Prime implicant quantifiers for matroids, graphs, and switching networks, Utilitas Math. 24 (1983), 155–163.Google Scholar
7. McKee, T. A., Duality principles for binary matroids and graphs, Discrete Math., 43 (1983), 215–222.Google Scholar
8. McKee, T. A., Series-parallel graphs: a logical approach, J. Graph Theory, 7 (1983), 177–181.Google Scholar
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. 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. 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