Year: 2019
Type: preprint
Abstract: An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal problems for ordered and convex geometric graphs have a rich history with applications to a variety of problems in combinatorial geometry. In this paper, we consider analogous extremal problems for uniform hypergraphs, and determine the order of magnitude of the extremal function for various ordered and convex geometric paths and matchings. Our results generalize earlier works of Braß-Károlyi-Valtr, Capoyleas-Pach and Aronov-Dujmovič-Morin-Ooms-da Silveira. We also provide a new generalization of the Erd\H os-Ko-Rado theorem in the ordered setting.
Source: arXiv (Cornell University)
Institution: Miami University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1125387830, G1148188478, G1484483809, G1641911518, Extremal Problems on Graphs Related to Colorings and Cycle Structure, G1669288158, Extremal and Probabilistic Questions on Hypergraphs, G524954726, G5337878546, G5427180767, Extremal Questions for Hypergraphs, G636142707, Extremal problems for sparse hypergraphs and graphs, G8147474489
OpenAlex ID: W2951889420