AI 中文总结
本文研究图的广义全染色，证实了Borowiecki等人提出的平面图广义全染色仅需4种颜色的猜想，针对两类无限平面图族完成了验证。
AI 中文摘要
本文研究图的广义全染色，其中由顶点和边分别构成的颜色类导出森林，且关联的边/顶点接收不同颜色。M. Borowiecki与I. Broere在《哈密顿性与平面图的广义全染色》（《Discussiones Mathematicae Graph Theory》36卷，2016年，243-257页）中猜想，平面图的这类染色仅需4种颜色。我们针对两类无限平面图族证实了该猜想。
英文摘要
In this paper we study generalised total colourings of graphs where the colour classes formed by vertices and edges, respectively, induce forests, while incident edges/vertices receive distinct colours. In [M. Borowiecki and I. Broere, Hamiltonicity and Generalised Total Colourings of Planar Graphs, Discussiones Mathematicae Graph Theory 36 (2016) 243--257] it was conjectured that for planar graphs, four colours suffice for this type of colouring. We confirm this conjecture for two infinite families of planar graphs.
Comments12 pages, 7 color figures
