FINE STRUCTURE OF 4-CRITICAL TRIANGLE-FREE GRAPHS II. PLANAR TRIANGLE-FREE GRAPHS WITH TWO PRECOLORED 4-CYCLES

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10364958" target="_blank" >RIV/00216208:11320/17:10364958 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/15M1023397" target="_blank" >http://dx.doi.org/10.1137/15M1023397</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/15M1023397" target="_blank" >10.1137/15M1023397</a>

Jazyk výsledku

angličtina

Název v původním jazyce

FINE STRUCTURE OF 4-CRITICAL TRIANGLE-FREE GRAPHS II. PLANAR TRIANGLE-FREE GRAPHS WITH TWO PRECOLORED 4-CYCLES

Popis výsledku v původním jazyce

We study 3-coloring properties of triangle-free planar graphs G with two precolored 4-cycles C-1 and C-2 that are far apart. We prove that either every precoloring of C-1 boolean OR C-2 extends to a 3-coloring of G, or G contains one of two special substructures which uniquely determine which 3-colorings of C-1 boolean OR C-2 extend. As a corollary, we prove that there exists a constant D &gt; 0 such that if H is a planar triangle-free graph and if S subset of V(H) consists of vertices at pairwise distances at least D, then every precoloring of S extends to a 3-coloring of H. This gives a positive answer to a conjecture of Dvorak, Kral, and Thomas, and implies an exponential lower bound on the number of 3-colorings of triangle-free planar graphs of bounded maximum degree.

Název v anglickém jazyce

FINE STRUCTURE OF 4-CRITICAL TRIANGLE-FREE GRAPHS II. PLANAR TRIANGLE-FREE GRAPHS WITH TWO PRECOLORED 4-CYCLES

Popis výsledku anglicky

We study 3-coloring properties of triangle-free planar graphs G with two precolored 4-cycles C-1 and C-2 that are far apart. We prove that either every precoloring of C-1 boolean OR C-2 extends to a 3-coloring of G, or G contains one of two special substructures which uniquely determine which 3-colorings of C-1 boolean OR C-2 extend. As a corollary, we prove that there exists a constant D &gt; 0 such that if H is a planar triangle-free graph and if S subset of V(H) consists of vertices at pairwise distances at least D, then every precoloring of S extends to a 3-coloring of H. This gives a positive answer to a conjecture of Dvorak, Kral, and Thomas, and implies an exponential lower bound on the number of 3-colorings of triangle-free planar graphs of bounded maximum degree.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA14-19503S" target="_blank" >GA14-19503S: Barevnost a struktura grafů</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

—

Svazek periodika

31

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

865-874

Kód UT WoS článku

000404770300015

EID výsledku v databázi Scopus

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