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arXiv · 2106.16089

Burling graphs revisited, part II: Structure

Pegah Pournajafi·Nicolas Trotignon
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Abstract

The Burling sequence is a sequence of triangle-free graphs of increasing chromatic number. Any graph which is an induced subgraph of a graph in this sequence is called a Burling graph. These graphs have attracted some attention because they have geometric representations and because they provide counter-examples to several conjectures about bounding the chromatic number in classes of graphs. We recall an equivalent definition of Burling graphs from the first part of this work: the graphs derived from a tree. We then give several structural properties of derived graphs.

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Pegah Pournajafi, Nicolas Trotignon. 2023-09-07. Burling graphs revisited, part II: Structure. https://doi.org/10.1016/j.ejc.2023.103849.

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