Chromatic numbers, Buchstaber numbers and chordality of Bier spheresLimonchenko, Ivan (Avtor) Vavpetič, Aleš (Avtor) Bier sphereBuchstaber numberchordal graphchromatic numberstacked polytopeWe describe all the Bier spheres of dimension $d$ with chromatic number equal to $d+1$ and prove that all other $d$-dimensional Bier spheres have chromatic number equal to $d+2$, for any integer $d \ge 0$. Then we prove a general formula for complex and mod $p$ Buchstaber numbers of a Bier sphere ${\rm Bier}(K)$, for each prime $p \in {\mathbb N}$ in terms of the $f$-vector of the underlying simplicial complex $K$. Finally, we classify all chordal Bier spheres and obtain their canonical realizations as boundaries of stacked polytopes.20262026-05-06 09:22:00Neznano29281UDK: 519.17:514ISSN pri članku: 0012-365XDOI: 10.1016/j.disc.2026.115189COBISS_ID: 277148675sl