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%2F23%3A10473769" target="_blank" >RIV/00216208:11320/23:10473769 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=recjS6~p92" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=recjS6~p92</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jctb.2020.09.003" target="_blank" >10.1016/j.jctb.2020.09.003</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 approximat-ing 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 K4k+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 K4k+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.Furthermore, we give somewhat weaker non-approximability bound for K4k+1-minor-free graphs with no cliques of size 4. On the positive side, we present 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.(c) 2020 Elsevier Inc. All rights reserved.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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