Connected greedy colouring in claw-free graphs
Discrete Mathematics
2018-06-08 v1 Combinatorics
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.
Cite
@article{arxiv.1805.01953,
title = {Connected greedy colouring in claw-free graphs},
author = {Ngoc Khang Le and Nicolas Trotignon},
journal= {arXiv preprint arXiv:1805.01953},
year = {2018}
}