A Note on Colourings of Connected $2$-edge Coloured Cubic Graphs

TL;DR

This paper proves that every connected 2-edge coloured cubic graph can be coloured with at most 10 colours, improving the known upper bound for their chromatic number.

Contribution

It establishes a new upper bound of 10 colours for the chromatic number of connected 2-edge coloured cubic graphs, reducing previous bounds.

Findings

Every connected 2-edge coloured cubic graph admits a 10-colouring.

The result improves the upper bound for the chromatic number.

Provides a tighter constraint on colourings of such graphs.

Abstract

In this short note we show that every connected $2$-edge coloured cubic graph admits an $10$-colouring. This lowers the best known upper bound for the chromatic number of connected $2$-edge coloured cubic graphs.