Equating three degrees of graphs

In this paper, we prove that, for every graph with at least 5 vertices, one can delete at most 3 vertices such that the subgraph obtained has at least three vertices with the same degree. This solves an open problem of Caro, Shapira and Yuster [Electron. J. Combin. 21 (2014) P1.24].

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Publication Details

Journal
ArXiv.org
Published
2025-05-01
Primary Topic
Limits and Structures in Graph Theory
Type
article
Field-Weighted Citation Impact
0.00

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article

Equating three degrees of graphs

ArXiv.org
Limits and Structures in Graph Theory
article

Equating three degrees of graphs

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Abstract

In this paper, we prove that, for every graph with at least 5 vertices, one can delete at most 3 vertices such that the subgraph obtained has at least three vertices with the same degree. This solves an open problem of Caro, Shapira and Yuster [Electron. J. Combin. 21 (2014) P1.24].

ArXiv.org
Center for Discrete Mathematics and Theoretical Computer Science (US)
National Natural Science Foundation of China
Openalex Percentile: Top 43%
Limits and Structures in Graph Theory
Open Access PDFOpenAlex
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Equating three degrees of graphs · ArXiv.org (2025) | TGRS Research Map | TGRS