1-Subdivisions, the Fractional Chromatic Number and the Hall Ratio

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10437056" target="_blank" >RIV/00216208:11320/20:10437056 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vCQ5MJzYe0" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vCQ5MJzYe0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00493-020-4223-9" target="_blank" >10.1007/s00493-020-4223-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

1-Subdivisions, the Fractional Chromatic Number and the Hall Ratio

Popis výsledku v původním jazyce

The Hall ratio of a graph G is the maximum of |V(H)|/α(H) over all subgraphs H of G. It is easy to see that the Hall ratio of a graph is a lower bound for the fractional chromatic number. It has been asked whether conversely, the fractional chromatic number is upper bounded by a function of the Hall ratio. We answer this question in negative, by showing two results of independent interest regarding 1-subdivisions (the 1-subdivision of a graph is obtained by subdividing each edge exactly once). For every c &gt; 0, every graph of sufficiently large average degree contains as a subgraph the 1-subdivision of a graph of fractional chromatic number at least c. For every d &gt; 0, there exists a graph G of average degree at least d such that every graph whose 1-subdivision appears as a subgraph of G has Hall ratio at most 18. We also discuss the consequences of these results in the context of graph cl

Název v anglickém jazyce

1-Subdivisions, the Fractional Chromatic Number and the Hall Ratio

Popis výsledku anglicky

The Hall ratio of a graph G is the maximum of |V(H)|/α(H) over all subgraphs H of G. It is easy to see that the Hall ratio of a graph is a lower bound for the fractional chromatic number. It has been asked whether conversely, the fractional chromatic number is upper bounded by a function of the Hall ratio. We answer this question in negative, by showing two results of independent interest regarding 1-subdivisions (the 1-subdivision of a graph is obtained by subdividing each edge exactly once). For every c &gt; 0, every graph of sufficiently large average degree contains as a subgraph the 1-subdivision of a graph of fractional chromatic number at least c. For every d &gt; 0, there exists a graph G of average degree at least d such that every graph whose 1-subdivision appears as a subgraph of G has Hall ratio at most 18. We also discuss the consequences of these results in the context of graph cl

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

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

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

Combinatorica

ISSN

0209-9683

e-ISSN

—

Svazek periodika

40

Číslo periodika v rámci svazku

august 2020

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

16

Strana od-do

759-774

Kód UT WoS článku

000558159600003

EID výsledku v databázi Scopus

2-s2.0-85089118333