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Maximum Matching in Regular and Almost Regular Graphs

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Abstract

We present an O(n 2logn)-time algorithm that finds a maximum matching in a regular graph with n vertices. More generally, the algorithm runs in O(rn 2logn) time if the difference between the maximum degree and the minimum degree is less than r. This running time is faster than applying the fastest known general matching algorithm that runs in \(O(\sqrt{n}m)\)-time for graphs with m edges, whenever m=ω(rn 1.5logn).

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References

  1. Biedl, T.C., Bose, P., Demaine, E.D., Lubiw, A.: Efficient algorithms for Petersen’s matching theorem. In: Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 130–139. SIAM, Philadelphia (1999)

    Google Scholar 

  2. Blum, N.: A new approach to maximum matching in general graphs. In: Proceedings of the 17th International Colloquium on Automata, Languages and Programming (ICALP), pp. 586–597 (1990)

    Chapter  Google Scholar 

  3. Bollobás, B.: Extremal Graph Theory. Academic Press, San Diego (1978)

    MATH  Google Scholar 

  4. Cole, R., Ost, K., Schirra, S.: Edge-coloring bipartite multigraphs in o(elogd) time. Combinatorica 21(1), 5–12 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Edmonds, J.: Paths, trees, and flowers. Can. J. Math. 17(3), 449–467 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gabow, H.N., Kariv, O.: Algorithms for edge coloring bipartite graphs and multigraphs. SIAM J. Comput. 11, 117 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gabow, H.N., Tarjan, R.E.: Faster scaling algorithms for general graph matching problems. J. ACM 38(4), 815–853 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  8. Goel, A., Kapralov, M., Khanna, S.: Perfect matchings in o(nlogn) time in regular bipartite graphs. In: Proceedings of the 42nd ACM Symposium on Theory of Computing (STOC), pp. 39–46. ACM, New York (2010).

    Chapter  Google Scholar 

  9. Goel, A., Kapralov, M., Khanna, S.: Perfect matchings via uniform sampling in regular bipartite graphs. ACM Trans. Algorithms (TALG) 6(2), 1–13 (2010)

    Article  MathSciNet  Google Scholar 

  10. Hopcroft, J.E., Karp, R.M.: An n 5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2, 225 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  11. Micali, S., Vazirani, V.: An \(O(\sqrt{(}|V|) |E|)\) algorithm for finding maximum matching in general graphs. In: Proceedings of the 21st Annual Symposium on Foundations of Computer Science (FOCS), pp. 17–27 (1980)

    Google Scholar 

  12. Vazirani, V.: A theory of alternating paths and blossoms for proving correctness of the general graph maximum matching algorithm. Combinatorica 14(1), 71–109 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  13. Vizing, V.G.: On an estimate of the chromatic class of a p-graph. Diskretn. Anal. 3(7), 23–30 (1964)

    MathSciNet  Google Scholar 

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  1. Department of Mathematics, University of Haifa, Haifa, 31905, Israel

    Raphael Yuster

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  1. Raphael Yuster
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Correspondence to Raphael Yuster.

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Yuster, R. Maximum Matching in Regular and Almost Regular Graphs. Algorithmica 66, 87–92 (2013). https://doi.org/10.1007/s00453-012-9625-7

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  • DOI: https://doi.org/10.1007/s00453-012-9625-7

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