Spectrally degenerate graphs: Hereditary case

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Spectrally degenerate graphs: Hereditary case
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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