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MiS Preprint
8/2023

Maximal colourings for graphs

Raffaella Mulas

Abstract

We consider two different notions of graph colouring, namely, the $t$-periodic colouring for vertices that has been introduced in 1974 by Bondy and Simonovits, and the periodic colouring for oriented edges that has been recently introduced in the context of spectral theory of non-backtracking operators. For each of these two colourings, we introduce the corresponding colouring number which is given by maximising the possible number of colours. We first investigate these two new colouring numbers individually, and we then show that there is a deep relationship between them.

Received:
Jul 21, 2023
Published:
Jul 21, 2023

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Preprint
2023 Repository Open Access
Raffaella Mulas

Maximal colourings for graphs