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A Combinatorial Algorithm to Find a Maximum Even Factor

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Integer Programming and Combinatorial Optimization (IPCO 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3509))

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Abstract

We give a new, algorithmic proof for the maximum even factor formula which can be converted into a polynomial time combinatorial algorithm to solve the maximum even factor problem. In several aspects, the approach is similar to Edmonds’ Matching Algorithm, but there is a significant difference.

Research supported by the Hungarian National Foundation for Scientific Research Grant, OTKA T037547.

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References

  1. Balas, E., Pulleyblank, W.: The perfectly matchable subgraph polytope of an arbitrary graph. Combinatorica 9, 321–337 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. Berge, C.: Sur le couplage maximum d’un graph. Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences 247, 258–259 (1958)

    MATH  MathSciNet  Google Scholar 

  3. Cunningham, W.H.: Matching, Matroids and Extensions. Math. Program. Ser. B 91(3), 515–542 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cunningham, W.H., Geelen, J.F.: The Optimal Path-Matching Problem. Combinatorica 17/3, 315–336 (1997)

    Article  MathSciNet  Google Scholar 

  5. Cunningham, W.H., Geelen, J.F.: Combinatorial Algorithms for Path–Matching. manuscript (2000)

    Google Scholar 

  6. Edmonds, J.: Paths, trees, and flowers. Canadian Journal of Mathematics 17, 449–467 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gallai, T.: Maximale Systeme unabhängiger Kanten. A Magyar Tudományos Akadémia Matematika Kutatóintézetének Közleményei 9, 401–413 (1964)

    MATH  MathSciNet  Google Scholar 

  8. Frank, A., Szegő, L.: A Note on the Path-Matching Formula. J. of Graph Theory 41/2, 110–119 (2002)

    Article  Google Scholar 

  9. Lovász, L.: On determinants, matchings and random algorithms. In: Budach, L. (ed.) Fundamentals of Computational Theory, pp. 565–574. Akademie-Verlag, Berlin (1979)

    Google Scholar 

  10. Lovász, L., Plummer, M.D.: Matching Theory. Akadémiai Kiadó, Budapest (1986)

    Google Scholar 

  11. Király, T., Makai, M.: On polyhedra related to even factors, EGRES Technical Report TR-2003-09

    Google Scholar 

  12. Pap, G., Szegő, L.: On the Maximum Even Factor in Weakly Symmetric Graphs. Journal of Combinatorial Theory Ser. B 91/2, 201–213 (2004)

    Article  Google Scholar 

  13. Spille, B., Szegő, L.: A Gallai-Edmonds-type Structure Theorem for Path-Matchings. Journal of Graph Theory 46/2, 93–102 (2004)

    Article  Google Scholar 

  14. Spille, B., Weismantel, R.: A Generalization of Edmonds’ matching and matroid intersection algorithms. In: Cook, W.J., Schultz, A.S. (eds.) Proceedings of the 9th International IPCO Conference (2002)

    Google Scholar 

  15. Tutte, W.T.: The factorization of linear graphs. The Journal of the London Mathematical Society 22, 107–111 (1947)

    Article  MATH  MathSciNet  Google Scholar 

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Pap, G. (2005). A Combinatorial Algorithm to Find a Maximum Even Factor. In: Jünger, M., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496915_6

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  • DOI: https://doi.org/10.1007/11496915_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26199-5

  • Online ISBN: 978-3-540-32102-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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