Burling graphs revisited, part II: Structure
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866912258722889728 |
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| author | Pournajafi, Pegah Trotignon, Nicolas |
| author_facet | Pournajafi, Pegah Trotignon, Nicolas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_16089 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Burling graphs revisited, part II: Structure Pournajafi, Pegah Trotignon, Nicolas Combinatorics 05C15 G.2.2 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. |
| title | Burling graphs revisited, part II: Structure |
| topic | Combinatorics 05C15 G.2.2 |
| url | https://arxiv.org/abs/2106.16089 |