Avoidability beyond paths
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910913158709248 |
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| author | Gurvich, Vladimir Krnc, Matjaž Milanič, Martin Vyalyi, Mikhail |
| author_facet | Gurvich, Vladimir Krnc, Matjaž Milanič, Martin Vyalyi, Mikhail |
| contents | The concept of avoidable paths in graphs was introduced by Beisegel, Chudnovsky, Gurvich, Milanič, and Servatius in 2019 as a common generalization of avoidable vertices and simplicial paths. In 2020, Bonamy, Defrain, Hatzel, and Thiebaut proved that every graph containing an induced path of order $k$ also contains an avoidable induced path of the same order. They also asked whether one could generalize this result to other avoidable structures, leaving the notion of avoidability up to interpretation. In this paper we address this question: we specify the concept of avoidability for arbitrary graphs equipped with two terminal vertices. We provide both positive and negative results, some of which appear to be related to the recent work by Chudnovsky, Norin, Seymour, and Turcotte [arXiv:2301.13175]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12803 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Avoidability beyond paths Gurvich, Vladimir Krnc, Matjaž Milanič, Martin Vyalyi, Mikhail Combinatorics Discrete Mathematics 05C75, 05C38 The concept of avoidable paths in graphs was introduced by Beisegel, Chudnovsky, Gurvich, Milanič, and Servatius in 2019 as a common generalization of avoidable vertices and simplicial paths. In 2020, Bonamy, Defrain, Hatzel, and Thiebaut proved that every graph containing an induced path of order $k$ also contains an avoidable induced path of the same order. They also asked whether one could generalize this result to other avoidable structures, leaving the notion of avoidability up to interpretation. In this paper we address this question: we specify the concept of avoidability for arbitrary graphs equipped with two terminal vertices. We provide both positive and negative results, some of which appear to be related to the recent work by Chudnovsky, Norin, Seymour, and Turcotte [arXiv:2301.13175]. |
| title | Avoidability beyond paths |
| topic | Combinatorics Discrete Mathematics 05C75, 05C38 |
| url | https://arxiv.org/abs/2208.12803 |