Proof of a conjecture of Xiao and Zamora

Wanfang Chen; Changhong Lu; Jia Bao Yang; Long Tu Yuan

doi:10.1007/s00373-025-02972-z

Proof of a conjecture of Xiao and Zamora

Wanfang Chen
, Changhong Lu
, Jia Bao Yang
, Long Tu Yuan^*

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University
Nanjing University

Research output: Contribution to journal › Article › peer-review

Abstract

A wheel, defined by Tutte, is the graph obtained from a circle by adding one new vertex and joining this vertex to all vertices of the circle. We determine the maximum number of edges in a graph which does not contain vertex-disjoint wheels. This confirms a conjecture posed by Xiao and Zamora in a stronger form.

Original language	English
Article number	114
Journal	Graphs and Combinatorics
Volume	41
Issue number	6
DOIs	https://doi.org/10.1007/s00373-025-02972-z
State	Published - Dec 2025

Keywords

Erdős-Simonovits stability theorem
Turán number
Wheels

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10.1007/s00373-025-02972-z

Cite this

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title = "Proof of a conjecture of Xiao and Zamora",

abstract = "A wheel, defined by Tutte, is the graph obtained from a circle by adding one new vertex and joining this vertex to all vertices of the circle. We determine the maximum number of edges in a graph which does not contain vertex-disjoint wheels. This confirms a conjecture posed by Xiao and Zamora in a stronger form.",

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author = "Wanfang Chen and Changhong Lu and Yang, \{Jia Bao\} and Yuan, \{Long Tu\}",

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AU - Lu, Changhong

AU - Yang, Jia Bao

AU - Yuan, Long Tu

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Japan KK 2025.

PY - 2025/12

Y1 - 2025/12

N2 - A wheel, defined by Tutte, is the graph obtained from a circle by adding one new vertex and joining this vertex to all vertices of the circle. We determine the maximum number of edges in a graph which does not contain vertex-disjoint wheels. This confirms a conjecture posed by Xiao and Zamora in a stronger form.

AB - A wheel, defined by Tutte, is the graph obtained from a circle by adding one new vertex and joining this vertex to all vertices of the circle. We determine the maximum number of edges in a graph which does not contain vertex-disjoint wheels. This confirms a conjecture posed by Xiao and Zamora in a stronger form.

KW - Erdős-Simonovits stability theorem

KW - Turán number

KW - Wheels

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Proof of a conjecture of Xiao and Zamora

Abstract

Keywords

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