t-Strong cliques and the degree-diameter problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00112696" target="_blank" >RIV/00216224:14330/19:00112696 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1258/762" target="_blank" >http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1258/762</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

t-Strong cliques and the degree-diameter problem

Popis výsledku v původním jazyce

For a graph G, L(G)(t) is the t-th power of the line graph of G that is, vertices of L(G)(t) are edges of G and two edges e, f is an element of 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 t-strong 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 t-strong chromatic index and t-strong clique are problems related to two famous problems: the conjecture of Erdos and NeAetfil 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)). We also show results for some special classes of graphs: K-1,K-r-free graphs and graphs with a large girth.

Název v anglickém jazyce

t-Strong cliques and the degree-diameter problem

Popis výsledku anglicky

For a graph G, L(G)(t) is the t-th power of the line graph of G that is, vertices of L(G)(t) are edges of G and two edges e, f is an element of 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 t-strong 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 t-strong chromatic index and t-strong clique are problems related to two famous problems: the conjecture of Erdos and NeAetfil 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)). We also show results for some special classes of graphs: K-1,K-r-free graphs and graphs with a large girth.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF16_027%2F0008360" target="_blank" >EF16_027/0008360: Postdoc@MUNI</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Acta Mathematica Universitatis Comenianae

ISSN

0231-6986

e-ISSN

0862-9544

Svazek periodika

88

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

5

Strana od-do

1057-1061

Kód UT WoS článku

000484349000109

EID výsledku v databázi Scopus

2-s2.0-85074006394