On a conjecture of Nikiforov involving a spectral radius condition for a graph to contain all trees

Xiangxiang Liu; Hajo Broersma; Ligong Wang

doi:10.1016/j.disc.2022.113112

On a conjecture of Nikiforov involving a spectral radius condition for a graph to contain all trees

Xiangxiang Liu
, Hajo Broersma
, Ligong Wang

数学与统计学院

Northwestern Polytechnical University Xian
University of Twente

科研成果: 期刊稿件 › 文章 › 同行评审

6 引用（Scopus）

摘要

We partly confirm a Brualdi-Solheid-Turán type conjecture due to Nikiforov, which is a spectral radius analogue of the well-known Erdős-Sós Conjecture that any tree of order t is contained in a graph of average degree greater than t−2. We confirm Nikiforov's Conjecture for all brooms and for a larger class of spiders. For our proofs we also obtain a new Turán type result which might turn out to be of independent interest.

源语言	英语
文章编号	113112
期刊	Discrete Mathematics
卷	345
期	12
DOI	https://doi.org/10.1016/j.disc.2022.113112
出版状态	已出版 - 12月 2022

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10.1016/j.disc.2022.113112

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abstract = "We partly confirm a Brualdi-Solheid-Tur{\'a}n type conjecture due to Nikiforov, which is a spectral radius analogue of the well-known Erd{\H o}s-S{\'o}s Conjecture that any tree of order t is contained in a graph of average degree greater than t−2. We confirm Nikiforov's Conjecture for all brooms and for a larger class of spiders. For our proofs we also obtain a new Tur{\'a}n type result which might turn out to be of independent interest.",

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AU - Liu, Xiangxiang

AU - Broersma, Hajo

AU - Wang, Ligong

PY - 2022/12

Y1 - 2022/12

N2 - We partly confirm a Brualdi-Solheid-Turán type conjecture due to Nikiforov, which is a spectral radius analogue of the well-known Erdős-Sós Conjecture that any tree of order t is contained in a graph of average degree greater than t−2. We confirm Nikiforov's Conjecture for all brooms and for a larger class of spiders. For our proofs we also obtain a new Turán type result which might turn out to be of independent interest.

AB - We partly confirm a Brualdi-Solheid-Turán type conjecture due to Nikiforov, which is a spectral radius analogue of the well-known Erdős-Sós Conjecture that any tree of order t is contained in a graph of average degree greater than t−2. We confirm Nikiforov's Conjecture for all brooms and for a larger class of spiders. For our proofs we also obtain a new Turán type result which might turn out to be of independent interest.

KW - Broom

KW - Brualdi-Solheid-Turán type problem

KW - Spectral radius

KW - Spider

UR - https://www.scopus.com/pages/publications/85135404460

U2 - 10.1016/j.disc.2022.113112

DO - 10.1016/j.disc.2022.113112

M3 - 文章

AN - SCOPUS:85135404460

SN - 0012-365X

VL - 345

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 12

M1 - 113112

ER -

On a conjecture of Nikiforov involving a spectral radius condition for a graph to contain all trees

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