FINE STRUCTURE OF 4-CRITICAL TRIANGLE-FREE GRAPHS I. PLANAR GRAPHS WITH TWO TRIANGLES AND 3-COLORABILITY OF CHAINS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10385413" target="_blank" >RIV/00216208:11320/18:10385413 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1137/15M1023385" target="_blank" >https://doi.org/10.1137/15M1023385</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/15M1023385" target="_blank" >10.1137/15M1023385</a>

Jazyk výsledku

angličtina

Název v původním jazyce

FINE STRUCTURE OF 4-CRITICAL TRIANGLE-FREE GRAPHS I. PLANAR GRAPHS WITH TWO TRIANGLES AND 3-COLORABILITY OF CHAINS

Popis výsledku v původním jazyce

Aksenov proved that in a planar graph G with at most one triangle, every precoloring of a 4-cycle can be extended to a 3-coloring of G. We give an exact characterization of planar graphs with two triangles in which some precoloring of a 4-cycle does not extend. We apply this characterization to solve the precoloring extension problem from two 4-cycles in a triangle-free planar graph in the case that the precolored 4-cycles are separated by many disjoint 4-cycles. The latter result is used in follow-up papers [SIAM J. Discrete Math., 31 (2017), pp. 865-874; SIAM J. Discrete Math., 32 (2018), pp. 94-105] to give detailed information about the structure of 4-critical triangle-free graphs embedded in a fixed surface.

Název v anglickém jazyce

FINE STRUCTURE OF 4-CRITICAL TRIANGLE-FREE GRAPHS I. PLANAR GRAPHS WITH TWO TRIANGLES AND 3-COLORABILITY OF CHAINS

Popis výsledku anglicky

Aksenov proved that in a planar graph G with at most one triangle, every precoloring of a 4-cycle can be extended to a 3-coloring of G. We give an exact characterization of planar graphs with two triangles in which some precoloring of a 4-cycle does not extend. We apply this characterization to solve the precoloring extension problem from two 4-cycles in a triangle-free planar graph in the case that the precolored 4-cycles are separated by many disjoint 4-cycles. The latter result is used in follow-up papers [SIAM J. Discrete Math., 31 (2017), pp. 865-874; SIAM J. Discrete Math., 32 (2018), pp. 94-105] to give detailed information about the structure of 4-critical triangle-free graphs embedded in a fixed surface.

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

2018

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

32

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

31

Strana od-do

1775-1805

Kód UT WoS článku

000450810500012

EID výsledku v databázi Scopus

2-s2.0-85053937646