Additive non-approximability of chromatic number in proper minor-closed classes

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Additive non-approximability of chromatic number in proper minor-closed classes

Popis výsledku v původním jazyce

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 &gt; 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 &gt; 1 and 1 &lt; beta &lt; 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.

Název v anglickém jazyce

Additive non-approximability of chromatic number in proper minor-closed classes

Popis výsledku anglicky

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 &gt; 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 &gt; 1 and 1 &lt; beta &lt; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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/GA17-04611S" target="_blank" >GA17-04611S: Ramseyovské aspekty barvení grafů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Journal of Combinatorial Theory. Series B

ISSN

0095-8956

e-ISSN

1096-0902

Svazek periodika

158

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

74-92

Kód UT WoS článku

000901805500004

EID výsledku v databázi Scopus

2-s2.0-85091824420