Stable sets in flag spheres

Maria Chudnovsky; Eran Nevo

doi:10.1016/j.ejc.2023.103699

Stable sets in flag spheres

Maria Chudnovsky, Eran Nevo

Einstein Institute of Mathematics

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

Abstract

We provide lower and upper bounds on the minimum size of a maximum stable set over graphs of flag spheres, as a function of the dimension of the sphere and the number of vertices. Further, we use stable sets together with graph rigidity to obtain an improved Lower Bound Theorem for the face numbers of flag spheres. We propose a graph rigidity approach to settle the Lower Bound Conjecture for flag spheres in full.

Original language	English
Article number	103699
Pages (from-to)	1-9
Number of pages	9
Journal	European Journal of Combinatorics
Volume	110
DOIs	https://doi.org/10.1016/j.ejc.2023.103699
State	Published - May 2023

Bibliographical note

Funding Information:
Partially supported by NSF-EPSRC, UK-USA Grant DMS-2120644 and by ISF, Israel grant 2480/20.Partially supported by the Israel Science Foundation grant ISF-2480/20 and by ISF-BSF, Israel-US joint grant 2016288.

Publisher Copyright:
© 2023 Elsevier Ltd

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10.1016/j.ejc.2023.103699

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Stable sets in flag spheres

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