A note on degenerate and spectrally degenerate graphs

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Abstract

A graph G is called spectrally d-degenerate if the largest eigenvalue of each subgraph of it with maximum degree D is at most √dD. We prove that for every constant M there is a graph with minimum degree M, which is spectrally 50-degenerate. This settles a problem of Dvorák and Mohar (Spectrally degenerate graphs: Hereditary case, arXiv: 1010.3367).

Original languageEnglish (US)
Pages (from-to)1-6
Number of pages6
JournalJournal of Graph Theory
Volume72
Issue number1
DOIs
StatePublished - Jan 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • degenerate graphs
  • graph eigenvalues
  • spectral radius

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