Abstract
We give the first, as far as we know, feasible proof of König’s Min-Max Theorem (KMM), a fundamental result in combinatorial matrix theory, and we show the equivalence of KMM to various Min-Max principles, with proofs of low complexity.
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References
Aharoni, R.: Menger’s theorem for graphs containing no infinite paths. European Journal of Combinatorics 4, 201–204 (1983)
Brualdi, R.A., Ryser, H.J.: Combinatorial Matrix Theory. Cambridge University Press (1991)
Buss, S.R.: Bounded Arithmetic. Bibliopolis, Naples (1986)
Buss, S.R.: Axiomatizations and conservations results for fragments of Bounded Arithmetic. AMS Contemporary Mathematics 106, 57–84 (1990)
Cook, S.A., Nguyen, P.: Logical Foundations of Proof Complexity. Cambridge Univeristy Press (2010)
Dilworth, R.P.: A decomposition theorem for partially ordered sets. Annals of Mathematics 51(1), 161–166 (1950)
Everett, C.J., Whaples, G.: Representations of sequences of sets. American Journal of Mathematics 71(2), 287–293 (1949)
Göring, F.: Short proof of Menger’s theorem. Discrete Mathematics 219, 295–296 (2000)
Hall, P.: On representatives of subsets. In: Gessel, I., Rota, G.-C. (eds.) Classic Papers in Combinatorics. Modern Birkhäuser Classics, pp. 58–62. Birkhäuser, Boston (1987)
Halmos, P.R., Vaughan, H.E.: The marriage problem. American Journal of Mathematics 72(1), 214–215 (1950)
Lê, D.T.M., Cook, S.A.: Formalizing randomized matching algorithms. Logical Methods in Computer Science 8, 1–25 (2012)
Menger, K.: Zur allgemeinen kurventheorie. Fund. Math. 10, 95–115 (1927)
Perles, M.A.: A proof of dilworth’s decomposition theorem for partially ordered sets. Israel Journal of Mathematics 1, 105–107 (1963)
Pym, J.S.: A proof of Menger’s theorem. Monatshefte für Mathematik 73(1), 81–83 (1969)
Soltys, M., Cook, S.: The proof complexity of linear algebra. Annals of Pure and Applied Logic 130(1-3), 207–275 (2004)
Soltys, M.: Feasible proofs of Szpilrajn’s theorem: a proof-complexity framework for concurrent automata. Journal of Automata, Languages and Combinatorics (JALC) 16(1), 27–38 (2011)
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Fernández, A.G., Soltys, M. (2013). Feasible Combinatorial Matrix Theory. In: Chatterjee, K., Sgall, J. (eds) Mathematical Foundations of Computer Science 2013. MFCS 2013. Lecture Notes in Computer Science, vol 8087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40313-2_68
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DOI: https://doi.org/10.1007/978-3-642-40313-2_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40312-5
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