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B-coloring of MP2-graphs

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  • Chen, Dong
  • Wang, Weifan
  • Xu, Yitong

Abstract

A B-coloring is a proper edge-coloring in which the four edges of every 4-cycle receive four distinct colors, and qB(G) denotes the minimum number of colors in such colorings. We study B-colorings of maximal planar graphs with diameter two (MP2-graphs). It is shown that MP2-graphs with maximum degree Δ ≥ 5 satisfy qB(G) ≤ 2Δ, and this bound is tight. We further determine qB(G) for all MP2-graphs with 2 ≤ Δ ≤ 4. As a consequence, a conjecture of Gyárfás et al. (2024) is verified for this class of graphs.

Suggested Citation

  • Chen, Dong & Wang, Weifan & Xu, Yitong, 2026. "B-coloring of MP2-graphs," Applied Mathematics and Computation, Elsevier, vol. 531(C).
    • Handle: RePEc:eee:apmaco:v:531:y:2026:i:c:s0096300326002389
    DOI: 10.1016/j.amc.2026.130186
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