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A polynomial-time nearly-optimal algorithm for an edge coloring problem in outerplanar graphs

Author

Listed:
  • Weifan Wang

    (Zhejiang Normal University)

  • Danjun Huang

    (Zhejiang Normal University)

  • Yanwen Wang

    (Zhejiang Normal University)

  • Yiqiao Wang

    (Beijing University of Chinese Medicine)

  • Ding-Zhu Du

    (Ton Duc Thang University
    University of Texas at Dallas)

Abstract

Given a graph G, we study the problem of finding the minimum number of colors required for a proper edge coloring of G such that any pair of vertices at distance 2 have distinct sets consisting of colors of their incident edges. This minimum number is called the 2-distance vertex-distinguishing index, denoted by $$\chi '_{d2}(G)$$ χ d 2 ′ ( G ) . Using the breadth first search method, this paper provides a polynomial-time algorithm producing nearly-optimal solution in outerplanar graphs. More precisely, if G is an outerplanar graph with maximum degree $$\varDelta $$ Δ , then the produced solution uses colors at most $$\varDelta +8$$ Δ + 8 . Since $$\chi '_{d2}(G)\ge \varDelta $$ χ d 2 ′ ( G ) ≥ Δ for any graph G, our solution is within eight colors from optimal.

Suggested Citation

  • Weifan Wang & Danjun Huang & Yanwen Wang & Yiqiao Wang & Ding-Zhu Du, 2016. "A polynomial-time nearly-optimal algorithm for an edge coloring problem in outerplanar graphs," Journal of Global Optimization, Springer, vol. 65(2), pages 351-367, June.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:2:d:10.1007_s10898-015-0360-x
    DOI: 10.1007/s10898-015-0360-x
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    Cited by:

    1. Dan Yi & Junlei Zhu & Lixia Feng & Jiaxin Wang & Mengyini Yang, 2019. "Optimal r-dynamic coloring of sparse graphs," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 545-555, August.
    2. Victor Loumngam Kamga & Weifan Wang & Ying Wang & Min Chen, 2018. "2-Distance vertex-distinguishing index of subcubic graphs," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 108-120, July.

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