Intrinsically knotted graphs and connected domination
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909252375805952 |
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| author | Li, Gregory Pavelescu, Andrei Pavelescu, Elena |
| author_facet | Li, Gregory Pavelescu, Andrei Pavelescu, Elena |
| contents | We classify all the maximal linklessly embeddable graphs of order 12 and show that their complements are all intrinsically knotted. We derive results about the connected domination numbers of a graph and its complement. We provide an answer to an open question about the minimal order of a 3-non-compliant graph. We prove that the complements of knotlessly embeddable graphs of order at least 15 are all intrinsically knotted. We provide results on general $k$-non-compliant graphs and leave a set of open questions for further exploration of the subject. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intrinsically knotted graphs and connected domination Li, Gregory Pavelescu, Andrei Pavelescu, Elena Combinatorics Geometric Topology 05C10, 57M15 We classify all the maximal linklessly embeddable graphs of order 12 and show that their complements are all intrinsically knotted. We derive results about the connected domination numbers of a graph and its complement. We provide an answer to an open question about the minimal order of a 3-non-compliant graph. We prove that the complements of knotlessly embeddable graphs of order at least 15 are all intrinsically knotted. We provide results on general $k$-non-compliant graphs and leave a set of open questions for further exploration of the subject. |
| title | Intrinsically knotted graphs and connected domination |
| topic | Combinatorics Geometric Topology 05C10, 57M15 |
| url | https://arxiv.org/abs/2407.09476 |