Stable sets in flag spheres
Maria Chudnovsky, Eran Nevo
TL;DR
This paper investigates the size of maximum stable sets in graphs derived from flag spheres, establishing bounds and applying these results to improve face number bounds in geometric combinatorics.
Contribution
It introduces bounds on maximum stable set sizes in flag sphere graphs and uses these to enhance the Lower Bound Theorem for flag sphere face numbers.
Findings
Established bounds on stable set sizes in flag sphere graphs
Connected stable set properties to face number bounds in flag spheres
Improved the Lower Bound Theorem for flag sphere face numbers
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 to obtain an improved Lower Bound Theorem for the face numbers of flag spheres.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Limits and Structures in Graph Theory