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An optimal square coloring of planar graphs

Author

Listed:
  • Yuehua Bu

    (Zhejiang Normal University)

  • Xubo Zhu

    (Zhejiang Normal University)

Abstract

The square coloring of a graph is to color the vertices of a graph at distance at most 2 with different colors. In 1977, Wegner posed a conjecture on square coloring of planar graphs. The conjecture is still open. In this paper, we prove that Wegner’s conjecture is true for planar graphs with girth at least 6.

Suggested Citation

  • Yuehua Bu & Xubo Zhu, 2012. "An optimal square coloring of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 580-592, November.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:4:d:10.1007_s10878-011-9409-z
    DOI: 10.1007/s10878-011-9409-z
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    References listed on IDEAS

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    1. Peng-Jun Wan, 1997. "Near-Optimal Conflict-Free Channel Set Assignments for an Optical Cluster-Based Hypercube Network," Journal of Combinatorial Optimization, Springer, vol. 1(2), pages 179-186, June.
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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. Hoang La & Mickael Montassier, 2022. "2-Distance list $$(\Delta +2)$$ ( Δ + 2 ) -coloring of planar graphs with girth at least 10," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1356-1375, September.
    3. Wei Dong & Baogang Xu, 2017. "2-Distance coloring of planar graphs with girth 5," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1302-1322, November.
    4. Junlei Zhu & Yuehua Bu & Miltiades P. Pardalos & Hongwei Du & Huijuan Wang & Bin Liu, 2018. "Optimal channel assignment and L(p, 1)-labeling," Journal of Global Optimization, Springer, vol. 72(3), pages 539-552, November.
    5. Wei Dong & Wensong Lin, 2016. "An improved bound on 2-distance coloring plane graphs with girth 5," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 645-655, August.
    6. Yuehua Bu & Xiaoyan Yan, 2015. "List 2-distance coloring of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 1180-1195, November.
    7. Qiming Fang & Li Zhang, 2022. "Sharp upper bound of injective coloring of planar graphs with girth at least 5," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1161-1198, September.

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