Spectrally degenerate graphs: Hereditary case

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10125704" target="_blank" >RIV/00216208:11320/12:10125704 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jctb.2012.05.002" target="_blank" >http://dx.doi.org/10.1016/j.jctb.2012.05.002</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jctb.2012.05.002" target="_blank" >10.1016/j.jctb.2012.05.002</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Spectrally degenerate graphs: Hereditary case

Popis výsledku v původním jazyce

It is well known that the spectral radius of a tree whose maximum degree is Delta cannot exceed 2 root Delta - 1. A similar upper bound holds for arbitrary planar graphs, whose spectral radius cannot exceed root 8 Delta + 10, and more generally, for alld-degenerate graphs, where the corresponding upper bound is root 4d Delta. Following this, we say that a graph G is spectrally d-degenerate if every subgraph H of G has spectral radius at most root d Delta(H). In this paper we derive a rough converse ofthe above-mentioned results by proving that each spectrally d-degenerate graph G contains a vertex whose degree is at most 4d log(2)(Delta(G)/d) (if Delta(G) }= 2d). It is shown that the dependence on Delta in this upper bound cannot be eliminated, as long as the dependence on d is subexponential. It is also proved that the problem of deciding if a graph is spectrally d-degenerate is Co-NP-complete. (C) 2012 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Spectrally degenerate graphs: Hereditary case

Popis výsledku anglicky

It is well known that the spectral radius of a tree whose maximum degree is Delta cannot exceed 2 root Delta - 1. A similar upper bound holds for arbitrary planar graphs, whose spectral radius cannot exceed root 8 Delta + 10, and more generally, for alld-degenerate graphs, where the corresponding upper bound is root 4d Delta. Following this, we say that a graph G is spectrally d-degenerate if every subgraph H of G has spectral radius at most root d Delta(H). In this paper we derive a rough converse ofthe above-mentioned results by proving that each spectrally d-degenerate graph G contains a vertex whose degree is at most 4d log(2)(Delta(G)/d) (if Delta(G) }= 2d). It is shown that the dependence on Delta in this upper bound cannot be eliminated, as long as the dependence on d is subexponential. It is also proved that the problem of deciding if a graph is spectrally d-degenerate is Co-NP-complete. (C) 2012 Elsevier Inc. All rights reserved.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Journal of Combinatorial Theory. Series B

ISSN

0095-8956

e-ISSN

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Svazek periodika

102

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

11

Strana od-do

1099-1109

Kód UT WoS článku

000308258000004

EID výsledku v databázi Scopus

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