Strong Cliques in Claw-Free Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F21%3A00129837" target="_blank" >RIV/00216224:14330/21:00129837 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00373-021-02379-6" target="_blank" >http://dx.doi.org/10.1007/s00373-021-02379-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00373-021-02379-6" target="_blank" >10.1007/s00373-021-02379-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Strong Cliques in Claw-Free Graphs

Popis výsledku v původním jazyce

For a graph G, L(G)(2) is the square of the line graph of G - that is, vertices of L(G)(2) are edges of G and two edges e, f is an element of EoGTHORN are adjacent in L(G)(2) if at least one vertex of e is adjacent to a vertex of f and e not equal f. The strong chromatic index of G, denoted by s'(G), is the chromatic number of L(G)(2). A strong clique in G is a clique in L(G())2. Finding a bound for the maximum size of a strong clique in a graph with given maximum degree is a problem connected to a famous conjecture of Erdos and Nes. etr.il concerning strong chromatic index of graphs. In this note we prove that a size of a strong clique in a claw-free graph with maximum degree triangle is at most triangle(2) + 1/2 triangle. This result improves the only known result 1:125 triangle(2) + triangle, which is a bound for the strong chromatic index of claw-free graphs.

Název v anglickém jazyce

Strong Cliques in Claw-Free Graphs

Popis výsledku anglicky

For a graph G, L(G)(2) is the square of the line graph of G - that is, vertices of L(G)(2) are edges of G and two edges e, f is an element of EoGTHORN are adjacent in L(G)(2) if at least one vertex of e is adjacent to a vertex of f and e not equal f. The strong chromatic index of G, denoted by s'(G), is the chromatic number of L(G)(2). A strong clique in G is a clique in L(G())2. Finding a bound for the maximum size of a strong clique in a graph with given maximum degree is a problem connected to a famous conjecture of Erdos and Nes. etr.il concerning strong chromatic index of graphs. In this note we prove that a size of a strong clique in a claw-free graph with maximum degree triangle is at most triangle(2) + 1/2 triangle. This result improves the only known result 1:125 triangle(2) + triangle, which is a bound for the strong chromatic index of claw-free graphs.

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

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Graphs and Combinatorics

ISSN

0911-0119

e-ISSN

—

Svazek periodika

37

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

13

Strana od-do

2581-2593

Kód UT WoS článku

000676086900002

EID výsledku v databázi Scopus

2-s2.0-85111123933