Coloring near-quadrangulations of the cylinder and the torus

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10437031" target="_blank" >RIV/00216208:11320/21:10437031 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=c7RoMCpI5H" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=c7RoMCpI5H</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ejc.2020.103258" target="_blank" >10.1016/j.ejc.2020.103258</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Coloring near-quadrangulations of the cylinder and the torus

Popis výsledku v původním jazyce

Let G be a simple connected plane graph and let C-1 and C-2 be cycles in G bounding distinct faces f(1) and f(2). For a positive integer l, let r(l) denote the number of integers n such that -l &lt;= n &lt;= l, is divisible by 3, and n has the same parity as .e; in particular, r(4) = 1. Let r(f1), (f2) (G) = Pi(f) r (vertical bar f vertical bar), where the product is over the faces f of G distinct from f(1) and f(2) , and let q(G) = 1+ Sigma(f:vertical bar f vertical bar not equal 4 )vertical bar f vertical bar where the sum is over all faces f of G (of length other than four). We give an algorithm with time complexity O(r(f1,f2) (G)q(G)vertical bar G vertical bar) which, given a 3-coloring psi of C-1 boolean OR C-2, either finds an extension of psi to a 3-coloring of G, or correctly decides no such extension exists. The algorithm is based on a min-max theorem for a variant of integer 2-commodity flows, and consequently in the negative case produces an obstruction to the existence of the extension. As a corollary, we show that every triangle-free graph drawn in the torus with edge-width at least 21 is 3-colorable. (C) 2020 Elsevier Ltd. All rights reserved.

Název v anglickém jazyce

Coloring near-quadrangulations of the cylinder and the torus

Popis výsledku anglicky

Let G be a simple connected plane graph and let C-1 and C-2 be cycles in G bounding distinct faces f(1) and f(2). For a positive integer l, let r(l) denote the number of integers n such that -l &lt;= n &lt;= l, is divisible by 3, and n has the same parity as .e; in particular, r(4) = 1. Let r(f1), (f2) (G) = Pi(f) r (vertical bar f vertical bar), where the product is over the faces f of G distinct from f(1) and f(2) , and let q(G) = 1+ Sigma(f:vertical bar f vertical bar not equal 4 )vertical bar f vertical bar where the sum is over all faces f of G (of length other than four). We give an algorithm with time complexity O(r(f1,f2) (G)q(G)vertical bar G vertical bar) which, given a 3-coloring psi of C-1 boolean OR C-2, either finds an extension of psi to a 3-coloring of G, or correctly decides no such extension exists. The algorithm is based on a min-max theorem for a variant of integer 2-commodity flows, and consequently in the negative case produces an obstruction to the existence of the extension. As a corollary, we show that every triangle-free graph drawn in the torus with edge-width at least 21 is 3-colorable. (C) 2020 Elsevier Ltd. 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

2021

Kód důvěrnosti údajů

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

Název periodika

European Journal of Combinatorics

ISSN

0195-6698

e-ISSN

—

Svazek periodika

93

Číslo periodika v rámci svazku

March 2021

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

22

Strana od-do

103258

Kód UT WoS článku

000607517300008

EID výsledku v databázi Scopus

2-s2.0-85096197095