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%2F21%3A00129841" target="_blank" >RIV/00216224:14330/21:00129841 - isvavai.cz</a>

Výsledek na webu

<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>

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 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.

Název v anglickém jazyce

t-Strong Cliques and the Degree-Diameter Problem

Popis výsledku anglicky

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.

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

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

—

Svazek periodika

35

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

13

Strana od-do

3017-3029

Kód UT WoS článku

000736744500030

EID výsledku v databázi Scopus

2-s2.0-85150241307