Induced subgraphs with many repeated degrees

Yair Caro; Raphael Yuster

doi:10.1016/j.disc.2020.111828

Induced subgraphs with many repeated degrees

Yair Caro, Raphael Yuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Article number	111828
Journal	Discrete Mathematics
Volume	343
Issue number	5
DOIs	https://doi.org/10.1016/j.disc.2020.111828
State	Published - May 2020

Bibliographical note

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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10.1016/j.disc.2020.111828

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abstract = "Erd{\H o}s, 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.",

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N2 - 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.

AB - 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.

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JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

Induced subgraphs with many repeated degrees

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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