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Legally \((\varDelta +2)\)-Coloring Bipartite Outerplanar Graphs in Cubic Time

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Combinatorial Optimization and Applications

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9486))

Abstract

The 2-distance vertex-distinguishing index \(\chi '_{d2}(G)\) of a graph G is the least number of colors required for a proper edge coloring of G such that any pair of vertices at distance 2 have distinct sets of colors on their incident edges. Let G be a bipartite outerplanar graph of order n with maximum degree \(\varDelta \). We give an algorithm of time complexity \(O(n^3)\) to show that \(\chi '_{d2}(G) \le \varDelta +2\).

D. Huang—Research supported by NSFC (No.11301486) and ZJNSFC (No.LQ13A010009).

W. Wang—Research supported by NSFC (No.11371328).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Danjun Huang & Weifan Wang

  2. Institute of Mathematics, Academia Sinica, Taipei, 10617, Taiwan

    Ko-Wei Lih

Authors
  1. Danjun Huang
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  2. Ko-Wei Lih
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  3. Weifan Wang
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Corresponding author

Correspondence to Danjun Huang .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Marywood University, Scranton, Pennsylvania, USA

    Zaixin Lu

  2. North Carolina Central University, Durham, North Carolina, USA

    Donghyun Kim

  3. University of Texas at Dallas, Richardson, Texas, USA

    Weili Wu

  4. Texas Southern University, Houston, Texas, USA

    Wei Li

  5. University of Texas at Dallas, Richardson, Texas, USA

    Ding-Zhu Du

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© 2015 Springer International Publishing Switzerland

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Huang, D., Lih, KW., Wang, W. (2015). Legally \((\varDelta +2)\)-Coloring Bipartite Outerplanar Graphs in Cubic Time. In: Lu, Z., Kim, D., Wu, W., Li, W., Du, DZ. (eds) Combinatorial Optimization and Applications. Lecture Notes in Computer Science(), vol 9486. Springer, Cham. https://doi.org/10.1007/978-3-319-26626-8_45

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  • DOI: https://doi.org/10.1007/978-3-319-26626-8_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26625-1

  • Online ISBN: 978-3-319-26626-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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