Fractional coloring of planar graphs of girth five

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10416991" target="_blank" >RIV/00216208:11320/20:10416991 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=w.0uC6mv_r" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=w.0uC6mv_r</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/18M1214068" target="_blank" >10.1137/18M1214068</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Fractional coloring of planar graphs of girth five

Popis výsledku v původním jazyce

A graph G is (a : b)-colorable if there exists an assignment of b-element subsets of {1, ..., a} to vertices of G such that sets assigned to adjacent vertices are disjoint. We first show that for every triangle-free planar graph G and a vertex x is an element of V(G), the graph G has a set coloring phi by subsets of {1, ..., 6} such that vertical bar phi(v)vertical bar &gt;= 2 for v is an element of V(G) and vertical bar phi(x)vertical bar = 3. As a corollary, every triangle-free planar graph on n vertices is (6n : 2n + 1)-colorable. We further use this result to prove that for every Delta, there exists a constant M-Delta such that every planar graph G of girth at least five and maximum degree Delta is (6M(Delta) : 2M(Delta) + 1)-colorable. Consequently, planar graphs of girth at least five with bounded maximum degree Delta have fractional chromatic number at most 3 -3/2M(Delta)+1.

Název v anglickém jazyce

Fractional coloring of planar graphs of girth five

Popis výsledku anglicky

A graph G is (a : b)-colorable if there exists an assignment of b-element subsets of {1, ..., a} to vertices of G such that sets assigned to adjacent vertices are disjoint. We first show that for every triangle-free planar graph G and a vertex x is an element of V(G), the graph G has a set coloring phi by subsets of {1, ..., 6} such that vertical bar phi(v)vertical bar &gt;= 2 for v is an element of V(G) and vertical bar phi(x)vertical bar = 3. As a corollary, every triangle-free planar graph on n vertices is (6n : 2n + 1)-colorable. We further use this result to prove that for every Delta, there exists a constant M-Delta such that every planar graph G of girth at least five and maximum degree Delta is (6M(Delta) : 2M(Delta) + 1)-colorable. Consequently, planar graphs of girth at least five with bounded maximum degree Delta have fractional chromatic number at most 3 -3/2M(Delta)+1.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

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

2020

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

34

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

538-555

Kód UT WoS článku

000546886700026

EID výsledku v databázi Scopus

2-s2.0-85091395984