تقرير
Weak Coloring Numbers of Intersection Graphs
| العنوان: | Weak Coloring Numbers of Intersection Graphs |
|---|---|
| المؤلفون: | Dvořák, Zdeněk, Pekárek, Jakub, Ueckerdt, Torsten, Yuditsky, Yelena |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Computer Science - Computational Geometry, Computer Science - Discrete Mathematics |
| الوصف: | Weak and strong coloring numbers are generalizations of the degeneracy of a graph, where for each natural number $k$, we seek a vertex ordering such every vertex can (weakly respectively strongly) reach in $k$ steps only few vertices with lower index in the ordering. Both notions capture the sparsity of a graph or a graph class, and have interesting applications in the structural and algorithmic graph theory. Recently, the first author together with McCarty and Norin observed a natural volume-based upper bound for the strong coloring numbers of intersection graphs of well-behaved objects in $\mathbb{R}^d$, such as homothets of a centrally symmetric compact convex object, or comparable axis-aligned boxes. In this paper, we prove upper and lower bounds for the $k$-th weak coloring numbers of these classes of intersection graphs. As a consequence, we describe a natural graph class whose strong coloring numbers are polynomial in $k$, but the weak coloring numbers are exponential. We also observe a surprising difference in terms of the dependence of the weak coloring numbers on the dimension between touching graphs of balls (single-exponential) and hypercubes (double-exponential). |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2103.17094 |
| رقم الأكسشن: | edsarx.2103.17094 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |