Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/645
Title: Combinatorics of unavoidable complexes
Authors: Jelić Milutinović, Marija 
Jojić, Duško
Timotijević, Marinko
Vrećica, Siniša T.
Živaljević, Rade T.
Affiliations: Topology 
Issue Date: 1-Jan-2020
Journal: European Journal of Combinatorics
Abstract: 
The partition number π(K) of a simplicial complex K⊆2[n] is the minimum integer k such that for each partition A1⊎…⊎Ak=[n] of [n] at least one of the sets Ai is in K. A complex K is r-unavoidable if π(K)≤r. Simplicial complexes with small π(K) are important for applications of the “constraint method” (Blagojević et al., 2014) and serve as an input for the “index inequalities” (Jojić et al., 2018), such as (1.1). We introduce a “threshold characteristic” ρ(K) of K (Section 3) and define a fractional (linear programming) relaxation of π(K) (Section 4), which allows us to systematically generate interesting examples of r-unavoidable complexes and pave the way for new results of Van Kampen–Flores–Tverberg type.
URI: https://research.matf.bg.ac.rs/handle/123456789/645
ISSN: 01956698
DOI: 10.1016/j.ejc.2019.103004
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