On constrained intersection representations of graphs and digraphs

Ferdinando Cicalese; Clément Dallard; Martin Milanič

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arXiv · 2504.18365

On constrained intersection representations of graphs and digraphs

Ferdinando Cicalese·Clément Dallard·Martin Milanič

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Abstract

We study the problem of determining optimal directed intersection representations of DAGs in a model introduced by Kostochka, Liu, Machado, and Milenkovic [ISIT2019]: vertices are assigned color sets so that there is an arc from a vertex $u$ to a vertex $v$ if and only if their color sets have nonempty intersection and $v$ gets assigned strictly more colors than $u$, and the goal is to minimize the total number of colors. We show that the problem is polynomially solvable in the class of triangle-free and Hamiltonian DAGs and also disclose the relationship of this problem with several other models of intersection representations of graphs and digraphs.

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BibTeX RIS

Ferdinando Cicalese, Clément Dallard, Martin Milanič. 2025-04-25. On constrained intersection representations of graphs and digraphs. https://arxiv.org/abs/2504.18365

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