Strong Cliques in Claw-Free Graphs
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Strong Cliques in Claw-Free Graphs
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Graphs and Combinatorics
ISSN
0911-0119
e-ISSN
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Volume of the periodical
37
Issue of the periodical within the volume
6
Country of publishing house
DE - GERMANY
Number of pages
13
Pages from-to
2581-2593
UT code for WoS article
000676086900002
EID of the result in the Scopus database
2-s2.0-85111123933