Every plane graph of maximum degree 8 has an edge-face 9-colouring
Ross J. Kang, Jean-S\'ebastien Sereni, Mat\v{e}j Stehl\'ik

TL;DR
This paper proves that every plane graph with maximum degree 8 can be edge-face coloured using 9 colours, extending previous results for higher degrees and filling a gap in graph colouring theory.
Contribution
The authors extend Borodin's edge-face colouring bound to include plane graphs with maximum degree 8, a case not previously established.
Findings
Edge-face colouring with 9 colours is possible for maximum degree 8 graphs.
The result completes the extension of Borodin's bound down to degree 8.
The proof advances understanding of colourings in planar graphs.
Abstract
An edge-face colouring of a plane graph with edge set and face set is a colouring of the elements of such that adjacent or incident elements receive different colours. Borodin proved that every plane graph of maximum degree can be edge-face coloured with colours. Borodin's bound was recently extended to the case where . In this paper, we extend it to the case .
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