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arXiv · 1805.01953

Connected greedy colouring in claw-free graphs

Ngoc Khang Le·Nicolas Trotignon
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Abstract

An ordering of the vertices of a graph is \emph{connected} if every vertex (but the first) has a neighbor among its predecessors. The greedy colouring algorithm of a graph with a connected order consists in taking the vertices in order, and assigning to each vertex the smallest available colour. A graph is \emph{good} if the greedy algorithm on every connected order gives every connected induced subgraph of it an optimal colouring. We give the characterization of good claw-free graphs in terms of minimal forbidden induced subgraphs.

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Ngoc Khang Le, Nicolas Trotignon. 2018-05-04. Connected greedy colouring in claw-free graphs. https://arxiv.org/abs/1805.01953

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