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Enumeration algorithm for the edge coloring problem on bipartite graphs

  • Graph Theory
  • Conference paper
  • First Online:
Combinatorics and Computer Science (CCS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1120))

Abstract

In this paper, we propose an algorithm for finding all the edge colorings in bipartite graphs. Our algorithm requires O(T(n, m, Δ)+K min{n 2+m,T(n,m,Δ)}) time and O(mΔ) space, where n denotes the number of vertices, m denotes the number of edges, Δ denotes the number of maximum degree, T(n,m,Δ) denotes the time complexity of an edge coloring algorithm, and K denotes the number of edge colorings.

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References

  1. Bondy,J.A., Murty,U.S.R.: Graph theory with applications. North-Holland (1976)

    Google Scholar 

  2. Cole,R., Hopcroft,J.: On Edge Coloring Bipartite Graphs. SIAM J.Comput. 11 (1982) 540–546

    Article  Google Scholar 

  3. Dempster,M.A.H.: Two algorithms for the time-table problem, Combinatorial Mathematics and its Applications(ed. D.J.A.Welsh). Academic Press New York (1971) 63–85

    Google Scholar 

  4. Fukuda,K., Matsui,T.: Finding All the Minimum Cost perfect Matchings in bipartite Graphs. Networks 22 (1992) 461–468

    Google Scholar 

  5. Fukuda,K., Matsui,T.: Finding All the Perfect Matchings in Bipartite Graphs. Appl. Math. Lett. 7 1 (1994) 15–18

    MathSciNet  Google Scholar 

  6. Gabow,H.N.: Using Euler Partitions to Edge Color Bipartite Multigraphs. Information J. Comput. and Information Sciences 5 (1976) 345–355

    Article  Google Scholar 

  7. Gabow,H.N., Kariv,O.: Algorithms for Edge Coloring Bipartite Graphs and Multigraphs. SIAM J. Comput. 11 (1982) 117–129

    Article  Google Scholar 

  8. Gonzalez,T., Sahni,S.: Open Shop Scheduling to Minimize Finish Time. J. ACM. 23 (1976) 665–679

    Article  Google Scholar 

  9. Greenwell,D.L., Kronk,H.V.: Uniquely Line Colorable Graphs. Canad. Math. Bull. 16 (1973) 525–529

    Google Scholar 

  10. König,D.: Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlhere. Math. Ann. 77 (1916) 453–465

    Article  Google Scholar 

  11. Tarjan,R.E.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1 (1972) 146–160

    Article  Google Scholar 

  12. Thomason,A.G.: Hamiltonian Cycles and Uniquely Edge Colourable Graphs. Ann. Discrete Math. 3 (1978) 259–268

    Google Scholar 

  13. Yoshida,Matsui.Y., Matsui,T.: Finding All the Edge Colorings in Bipartite Graphs. T.IEE. Japan 114-C 4 (1994) 444–449 (in Japanese)

    Google Scholar 

  14. de Werra,D.: On some combinatorial problems arising in scheduling. INFOR. 8 (1970) 165–175

    Google Scholar 

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Author information

Authors and Affiliations

  1. Tokyo Metropolitan University, 192-03, Tokyo, Japan

    Yasuko Matsui

  2. University of Tokyo, 113, Tokyo, Japan

    Tomomi Matsui

Authors
  1. Yasuko Matsui
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  2. Tomomi Matsui
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Editor information

Michel Deza Reinhardt Euler Ioannis Manoussakis

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© 1996 Springer-Verlag Berlin Heidelberg

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Matsui, Y., Matsui, T. (1996). Enumeration algorithm for the edge coloring problem on bipartite graphs. In: Deza, M., Euler, R., Manoussakis, I. (eds) Combinatorics and Computer Science. CCS 1995. Lecture Notes in Computer Science, vol 1120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61576-8_69

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  • DOI: https://doi.org/10.1007/3-540-61576-8_69

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61576-7

  • Online ISBN: 978-3-540-70627-4

  • eBook Packages: Springer Book Archive

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