Academic Journal
Weak saturation of multipartite hypergraphs ...
| Title: | Weak saturation of multipartite hypergraphs ... |
|---|---|
| Authors: | Bulavka, Denys, Tancer, Martin, Tyomkyn, Mykhaylo |
| Publisher Information: | arXiv |
| Publication Year: | 2021 |
| Collection: | DataCite Metadata Store (German National Library of Science and Technology) |
| Subject Terms: | Combinatorics math.CO, FOS Mathematics |
| Description: | Given $q$-uniform hypergraphs ($q$-graphs) $F,G$ and $H$, where $G$ is a spanning subgraph of $F$, $G$ is called weakly $H$-saturated in $F$ if the edges in $E(F)\setminus E(G)$ admit an ordering $e_1,\dots, e_k$ so that for all $i\in [k]$ the hypergraph $G\cup \{e_1,\dots,e_i\}$ contains an isomorphic copy of $H$ which in turn contains the edge $e_i$. The weak saturation number of $H$ in $F$ is the smallest size of an $H$-weakly saturated subgraph of $F$. Weak saturation was introduced by Bollobás in 1968, but despite decades of study our understanding of it is still limited. The main difficulty lies in proving lower bounds on weak saturation numbers, which typically withstands combinatorial methods and requires arguments of algebraic or geometrical nature. In our main contribution in this paper we determine exactly the weak saturation number of complete multipartite $q$-graphs in the directed setting, for any choice of parameters. This generalizes a theorem of Alon from 1985. Our proof combines the ... : 6 pages. We have improved the presentation. To appear in Combinatorica ... |
| Document Type: | article in journal/newspaper text |
| Language: | unknown |
| Relation: | https://dx.doi.org/10.1007/s00493-023-00049-0 |
| DOI: | 10.48550/arxiv.2109.03703 |
| Availability: | https://doi.org/10.48550/arxiv.2109.0370310.1007/s00493-023-00049-0 https://arxiv.org/abs/2109.03703 |
| Rights: | Creative Commons Attribution 4.0 International ; https://creativecommons.org/licenses/by/4.0/legalcode ; cc-by-4.0 |
| Accession Number: | edsbas.703F2C82 |
| Database: | BASE |
| Description not available. |