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An upper bound for the choice number of star edge coloring of graphs

Author

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  • Cai, Jiansheng
  • Yang, Chunhua
  • Yu, Jiguo

Abstract

The star chromatic index of a multigraph G, denoted χs′(G), is the minimum number of colors needed to properly color the edges of G such that no path or cycle of length four is bi-colored. A multigraph G is star k-edge-colorable if χs′(G)≤k. Dvořák et al. (2013) proved that every subcubic multigraph is star 7-edge-colorable. They conjectured in the same paper that every subcubic multigraph should be star 6-edge-colorable. In this paper, we consider this problem in a more general setting, we investigate star list edge coloring of general graph G and obtain an upper bound for the choice number of star edge coloring of graphs, namely, we proved that χsl′≤⌈2Δ32(1Δ+2)12+2Δ⌉.

Suggested Citation

  • Cai, Jiansheng & Yang, Chunhua & Yu, Jiguo, 2019. "An upper bound for the choice number of star edge coloring of graphs," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 588-593.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:588-593
    DOI: 10.1016/j.amc.2018.12.016
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    References listed on IDEAS

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    1. Wang, Yiqiao & Wang, Weifan & Wang, Ying, 2018. "Edge-partition and star chromatic index," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 480-489.
    2. Wang, Ying & Wang, Yiqiao & Wang, Weifan, 2019. "Star edge-coloring of graphs with maximum degree four," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 268-275.
    3. Jiansheng Cai & Xueliang Li & Guiying Yan, 2017. "Improved upper bound for the degenerate and star chromatic numbers of graphs," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 441-452, August.
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