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Coupon coloring of some special graphs

Author

Listed:
  • Yongtang Shi

    (Nankai University)

  • Meiqin Wei

    (Nankai University)

  • Jun Yue

    (Shandong Normal University)

  • Yan Zhao

    (Taizhou University)

Abstract

Let G be a graph without isolated vertices. A k-coupon coloring of G is a k-coloring of G such that the neighborhood of every vertex of G contains vertices of all colors from $$[k] =\{1, 2, \ldots , k\}$$ [ k ] = { 1 , 2 , … , k } , which was recently introduced by Chen, Kim, Tait and Verstraete. The coupon coloring number $$\chi _c(G)$$ χ c ( G ) of G is the maximum k for which a k-coupon coloring exists. In this paper, we mainly study the coupon coloring of some special classes of graphs. We determine the coupon coloring numbers of complete graphs, complete k-partite graphs, wheels, cycles, unicyclic graphs, bicyclic graphs and generalised $$\Theta $$ Θ -graphs.

Suggested Citation

  • Yongtang Shi & Meiqin Wei & Jun Yue & Yan Zhao, 2017. "Coupon coloring of some special graphs," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 156-164, January.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:1:d:10.1007_s10878-015-9942-2
    DOI: 10.1007/s10878-015-9942-2
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    References listed on IDEAS

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    1. Li, Shasha & Li, Xueliang & Shi, Yongtang, 2015. "Note on the complexity of deciding the rainbow (vertex-) connectedness for bipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 155-161.
    2. Min Chen & Geňa Hahn & André Raspaud & Weifan Wang, 2012. "Some results on the injective chromatic number of graphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 299-318, October.
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    Citations

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    Cited by:

    1. Gao, Zhipeng & Lei, Hui & Wang, Kui, 2020. "Rainbow domination numbers of generalized Petersen graphs," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Banerjee, S. & Henning, Michael A. & Pradhan, D., 2021. "Perfect Italian domination in cographs," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    3. Bermudo, Sergio & Higuita, Robinson A. & Rada, Juan, 2020. "Domination in hexagonal chains," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    4. Ma, Yuede & Cai, Qingqiong & Yao, Shunyu, 2019. "Integer linear programming models for the weighted total domination problem," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 146-150.
    5. Yue, Jun & Wei, Meiqin & Li, Min & Liu, Guodong, 2018. "On the double Roman domination of graphs," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 669-675.
    6. Chen, He & Jin, Zemin, 2017. "Coupon coloring of cographs," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 90-95.
    7. Li, Shasha & Zhao, Yan & Li, Fengwei & Gu, Ruijuan, 2019. "The generalized 3-connectivity of the Mycielskian of a graph," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 882-890.

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