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Linear amortized time enumeration algorithms for compatible Euler trails in edge-colored graphs

Author

Listed:
  • Yuhang Bai

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

  • Zhiwei Guo

    (Yan’an University)

  • Shenggui Zhang

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

  • Yandong Bai

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

Abstract

A compatible Euler trail (tour) in an edge-colored graph is an Euler trail (tour) in which each two edges traversed consecutively along the Euler trail (tour) have distinct colors. In this paper, we show that the problem of counting compatible Euler trails in edge-colored graphs is $$\#$$ # P-complete, and develop O(mN) time algorithms for enumerating compatible Euler trails (tours) in edge-colored graphs with m edges and N compatible Euler trails (tours). It is worth mentioning that our algorithms can run in O(N) time when there is no vertex v with degree 4 and maximum monochromatic degree 2.

Suggested Citation

  • Yuhang Bai & Zhiwei Guo & Shenggui Zhang & Yandong Bai, 2023. "Linear amortized time enumeration algorithms for compatible Euler trails in edge-colored graphs," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-20, March.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:2:d:10.1007_s10878-023-01005-w
    DOI: 10.1007/s10878-023-01005-w
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    References listed on IDEAS

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    1. Zhiwei Guo & Hajo Broersma & Ruonan Li & Shenggui Zhang, 2020. "Some algorithmic results for finding compatible spanning circuits in edge-colored graphs," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1008-1019, November.
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