Year: 2021
Type: preprint
Abstract: In this paper, pursuing the same line of ideas in the proof of an old longstanding open conjecture of \emph{Kadison-Singer} , we introduce a key lemma which we call it the interlacing lemma which indicates a necessary condition for having a real root for sums of polynomials with (at least) one real root. Then, as an immediate application of this simple but potentially useful lemma we characterize several class of graphs which have only clique roots. Finally, we conclude our paper with several interesting open problems and conjectures for interested readers.
Source: arXiv (Cornell University)
Author: Faal, Hossein Teimoori
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4389844909