Weak Coloring Numbers of Intersection Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10448437" target="_blank" >RIV/00216208:11320/22:10448437 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4230/LIPIcs.SoCG.2022.39" target="_blank" >https://doi.org/10.4230/LIPIcs.SoCG.2022.39</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.SoCG.2022.39" target="_blank" >10.4230/LIPIcs.SoCG.2022.39</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Weak Coloring Numbers of Intersection Graphs

Popis výsledku v původním jazyce

Weak and strong coloring numbers are generalizations of the degeneracy of a graph, where for a positive integer k, we seek a vertex ordering such that every vertex can (weakly respectively strongly) reach in k steps only few vertices that precede it in the ordering. Both notions capture the sparsity of a graph or a graph class, and have interesting applications in structural and algorithmic graph theory. Recently, Dvorák, McCarty, and Norin observed a natural volume-based upper bound for the strong coloring numbers of intersection graphs of well-behaved objects in Rd, such as homothets of a 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).

Název v anglickém jazyce

Weak Coloring Numbers of Intersection Graphs

Popis výsledku anglicky

Weak and strong coloring numbers are generalizations of the degeneracy of a graph, where for a positive integer k, we seek a vertex ordering such that every vertex can (weakly respectively strongly) reach in k steps only few vertices that precede it in the ordering. Both notions capture the sparsity of a graph or a graph class, and have interesting applications in structural and algorithmic graph theory. Recently, Dvorák, McCarty, and Norin observed a natural volume-based upper bound for the strong coloring numbers of intersection graphs of well-behaved objects in Rd, such as homothets of a 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).

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/LL2005" target="_blank" >LL2005: Algoritmy a složitost v rámci a nad omezenou expanzí</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-227-3

ISSN

—

e-ISSN

—

Počet stran výsledku

15

Strana od-do

1-15

Název nakladatele

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik

Místo vydání

Dagstuhl, Germany

Místo konání akce

Berlín

Datum konání akce

7. 6. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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