Boxicity, poset dimension, and excluded minors
Abstract
In this short note, we relate the boxicity of graphs (and the dimension of posets) with their generalized coloring parameters. In particular, together with known estimates, our results imply that any graph with no $K_t$minor can be represented as the intersection of $O(t^2\log t)$ interval graphs (improving the previous bound of $O(t^4)$), and as the intersection of $\tfrac{15}2 t^2$ circulararc graphs.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.00850
 Bibcode:
 2018arXiv180400850E
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 9 pages, 3 figures  final version