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Some results on the injective chromatic number of graphs

Author

Listed:
  • Min Chen

    (Zhejiang Normal University)

  • Geňa Hahn

    (Université de Montréal)

  • André Raspaud

    (Université Bordeaux I)

  • Weifan Wang

    (Zhejiang Normal University)

Abstract

A k-coloring of a graph G=(V,E) is a mapping c:V→{1,2,…,k}. The coloring c is injective if, for every vertex v∈V, all the neighbors of v are assigned with distinct colors. The injective chromatic number χ i (G) of G is the smallest k such that G has an injective k-coloring. In this paper, we prove that every K 4-minor free graph G with maximum degree Δ≥1 has $\chi_{i}(G)\le \lceil \frac{3}{2}\Delta\rceil$ . Moreover, some related results and open problems are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9386-2
    DOI: 10.1007/s10878-011-9386-2
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    Citations

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    Cited by:

    1. 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.
    2. Yuehua Bu & Kai Lu & Sheng Yang, 2015. "Two smaller upper bounds of list injective chromatic number," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 373-388, February.
    3. Qing Cui & Zhenmeng Han, 2024. "Injective edge-coloring of claw-free subcubic graphs," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-32, July.
    4. Yue, Jun & Zhang, Shiliang & Zhang, Xia, 2016. "Note on the perfect EIC-graphs," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 481-485.
    5. Cai, Jiansheng & Li, Wenwen & Cai, Wenjing & Dehmer, Matthias, 2023. "List injective coloring of planar graphs," Applied Mathematics and Computation, Elsevier, vol. 439(C).

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