t-Strong Cliques and the Degree-Diameter Problem

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F21%3A00129841" target="_blank" >RIV/00216224:14330/21:00129841 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1137/21M1406970" target="_blank" >http://dx.doi.org/10.1137/21M1406970</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/21M1406970" target="_blank" >10.1137/21M1406970</a>

Result language

angličtina

Original language name

t-Strong Cliques and the Degree-Diameter Problem

Original language description

For a graph G, L(G)t is the tth power of the line graph of G; that is, vertices of L(G)(t) are edges of G and two edges e, f epsilon E(G) are adjacent in L(G)(t) if G contains a path with at most t vertices that starts in a vertex of e and ends in a vertex of f. The distance-t chromatic index of G is the chromatic number of L(G)(t), and a t-strong clique in G is a clique in L(G)(t). Finding upper bounds for the distance-t chromatic index and t-strong clique are problems related to two famous problems: the conjecture of Erdos and Nesetril concerning the strong chromatic index, and the degree/diameter problem. We prove that the size of a t-strong clique in a graph with maximum degree Delta is at most 1.75(Delta)t + O (Delta(t-1)), and for bipartite graphs the upper bound is at most Delta(t) + O (Delta(t-1)). As a corollary, we obtain upper bounds of 1.881 Delta(t) + O (Delta(t-1)) and 1.9703 + O (Delta(t-1)) on the distance-t chromatic index of bipartite graphs and general graphs. We also show results for some special classes of graphs: K1,r-free graphs and graphs with a large girth.

Czech name

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Czech description

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Type

J_imp - 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)

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2021

Confidentiality

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

Name of the periodical

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

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Volume of the periodical

35

Issue of the periodical within the volume

4

Country of publishing house

GB - UNITED KINGDOM

Number of pages

13

Pages from-to

3017-3029

UT code for WoS article

000736744500030

EID of the result in the Scopus database

2-s2.0-85150241307