On constrained intersection representations of graphs and digraphs
Discrete Mathematics
2025-04-28 v1 Data Structures and Algorithms
Information Theory
Combinatorics
math.IT
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 to a vertex if and only if their color sets have nonempty intersection and gets assigned strictly more colors than , 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.
Cite
@article{arxiv.2504.18365,
title = {On constrained intersection representations of graphs and digraphs},
author = {Ferdinando Cicalese and Clément Dallard and Martin Milanič},
journal= {arXiv preprint arXiv:2504.18365},
year = {2025}
}