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

paper

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

arXiv:2112.13253 · doi:10.1016/j.disc.2022.113112

Abstract

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.