Year: 2025
Type: article
Abstract: The study of geometric hypergraphs gave rise to the notion of $ABAB$-free hypergraphs. A hypergraph $\mathcal{H}$ is called $ABAB$-free if there is an ordering of its vertices such that there are no hyperedges $A,B$ and vertices $v_1,v_2,v_3,v_4$ in this order satisfying $v_1,v_3\in A\setminus B$ and $v_2,v_4\in B\setminus A$. In this paper, we prove that it is NP-complete to decide if a hypergraph is $ABAB$-free. We show a number of analogous results for hypergraphs with similar forbidden patterns, such as $ABABA$-free hypergraphs. As an application, we show that deciding whether a hypergraph is realizable as the incidence hypergraph of points and pseudodisks is also NP-complete. Comment: 10 pages
DOI: 10.46298/dmtcs.14610
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funders: Magyar Tudományos Akadémia, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, Innovációs és Technológiai Minisztérium, Indraprastha Institute of Information Technology, Delhi, Nemzeti Kutatási, Fejlesztési és Innovaciós Alap, National Research, Development and Innovation Office, H2020 European Research Council, HORIZON EUROPE European Research Council
Awards: G1196578329, G134384773, G1960547982, G2008435032, G2190636616, G298428782, G3035116162, G3743470659, G3824814584, G4395645117, G4647131000, G4740494454, G4890443012, G5489890681, G5649146922, G5865157238, From Geometry to Combinatorics and Back: Escaping the Curse of Dimensionality, G7694217703, G802890732, Effective Random Methods in Discrete Mathematics, G8550484722, G878884674
OpenAlex ID: W4409767763