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arXiv · 2301.09493

Functionality of box intersection graphs

Clément Dallard·Vadim Lozin·Martin Milanič·Kenny Štorgel·Viktor Zamaraev
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Abstract

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 $\mathbb{R}^2$.

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Clément Dallard, Vadim Lozin, Martin Milanič, Kenny Štorgel, Viktor Zamaraev. 2023-01-23. Functionality of box intersection graphs. https://doi.org/10.1007/s00025-023-02075-2

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