Functionality of box intersection graphs
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912186591346688 |
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| author | Dallard, Clément Lozin, Vadim Milanič, Martin Štorgel, Kenny Zamaraev, Viktor |
| author_facet | Dallard, Clément Lozin, Vadim Milanič, Martin Štorgel, Kenny Zamaraev, Viktor |
| contents | Functionality is a graph complexity measure that extends a variety of parameters, such as vertex degree, degeneracy, clique-width, or twin-width. In the present paper, we show that functionality is bounded for box intersection graphs in $\mathbb{R}^1$, i.e. for interval graphs, and unbounded for box intersection graphs in $\mathbb{R}^3$. We also study a parameter known as symmetric difference, which is intermediate between twin-width and functionality, and show that this parameter is unbounded both for interval graphs and for unit box intersection graphs in $\mathbb{R}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09493 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Functionality of box intersection graphs Dallard, Clément Lozin, Vadim Milanič, Martin Štorgel, Kenny Zamaraev, Viktor Combinatorics Discrete Mathematics 05C75 (Primary) 05C62 (Secondary) Functionality is a graph complexity measure that extends a variety of parameters, such as vertex degree, degeneracy, clique-width, or twin-width. In the present paper, we show that functionality is bounded for box intersection graphs in $\mathbb{R}^1$, i.e. for interval graphs, and unbounded for box intersection graphs in $\mathbb{R}^3$. We also study a parameter known as symmetric difference, which is intermediate between twin-width and functionality, and show that this parameter is unbounded both for interval graphs and for unit box intersection graphs in $\mathbb{R}^2$. |
| title | Functionality of box intersection graphs |
| topic | Combinatorics Discrete Mathematics 05C75 (Primary) 05C62 (Secondary) |
| url | https://arxiv.org/abs/2301.09493 |