Coloring near-quadrangulations of the cylinder and the torus

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Coloring near-quadrangulations of the cylinder and the torus
Original language description
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 <= n <= 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.
Czech name
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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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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