Additive Non-Approximability of Chromatic Number in Proper Minor-Closed Classes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10385422" target="_blank" >RIV/00216208:11320/18:10385422 - isvavai.cz</a>
Result on the web
<a href="http://drops.dagstuhl.de/opus/volltexte/2018/9051" target="_blank" >http://drops.dagstuhl.de/opus/volltexte/2018/9051</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2018.47" target="_blank" >10.4230/LIPIcs.ICALP.2018.47</a>

Result language
angličtina
Original language name
Additive Non-Approximability of Chromatic Number in Proper Minor-Closed Classes
Original language description
Robin Thomas asked whether for every proper minor-closed class G, there exists a polynomial-time algorithm approximating the chromatic number of graphs from G up to a constant additive error independent on the class G. We show this is not the case: unless P=NP, for every integer k >= 1, there is no polynomial-time algorithm to color a K_{4k+1}-minor-free graph G using at most chi(G)+k-1 colors. More generally, for every k >= 1 and 1 <=beta <=4/3, there is no polynomial-time algorithm to color a K_{4k+1}-minor-free graph G using less than beta chi(G)+(4-3 beta)k colors. As far as we know, this is the first non-trivial non-approximability result regarding the chromatic number in proper minor-closed classes. We also give somewhat weaker non-approximability bound for K_{4k+1}-minor-free graphs with no cliques of size 4. On the positive side, we present an additive approximation algorithm whose error depends on the apex number of the forbidden minor, and an algorithm with additive error 6 under the additional assumption that the graph has no 4-cycles.
Czech name
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Czech description
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Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA17-04611S" target="_blank" >GA17-04611S: Ramsey-like aspects of graph coloring</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
45th International Colloquium on Automata, Languages, and Programming (ICALP 2018
ISBN
978-3-95977-076-7
ISSN
1868-8969
e-ISSN
neuvedeno
Number of pages
12
Pages from-to
1-12
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl, Germany
Event location
Prague, Czech Republi
Event date
Jul 9, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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