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

Xiangxiang Liu, Hajo Broersma, Ligong Wang

Research output: Working paperPreprintAcademic

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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\'os 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.
Original languageEnglish
PublisherArXiv.org
DOIs
Publication statusPublished - 25 Dec 2021

Keywords

  • math.CO

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