Abstract
In this paper, we investigate the Colourability problem for dually chordal graphs and some of its generalisations. We show that the problem remains NP-complete if limited to four colours. For the case of three colours, we present a simple linear time algorithm for dismantlable graphs (which include dually chordal graphs) and present an O(n3m) time algorithm for graphs with tree-breadth 1. Additionally, we show that a dually chordal graph is 3-colourable if and only if it is perfect and has no clique of size four.
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