Induced subgraphs with many repeated degrees

Yair Caro, Raphael Yuster

Research output: Contribution to journalArticlepeer-review

Abstract

Erdős, Fajtlowicz and Staton asked for the least integer f(k) such that every graph with more than f(k) vertices has an induced regular subgraph with at least k vertices. Here we consider the following relaxed notions. Let g(k) be the least integer such that every graph with more than g(k) vertices has an induced subgraph with at least k repeated degrees and let h(k) be the least integer such that every graph with more than h(k) vertices has an induced subgraph with at least k maximum degree vertices. We obtain polynomial lower bounds for h(k) and g(k) and nontrivial linear upper bounds when the host graph has bounded maximum degree.

Original languageEnglish
Article number111828
JournalDiscrete Mathematics
Volume343
Issue number5
DOIs
StatePublished - May 2020

Bibliographical note

Funding Information:
Research supported in part by the Israel Science Foundation (grant No. 1082/16).

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

  • Degree repetition
  • Induced subgraph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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