On saturation of Berge hypergraphs
نویسندگان
چکیده
A hypergraph H=(V(H),E(H)) is a Berge copy of graph F, if V(F)⊂V(H) and there bijection f:E(F)→E(H) such that for any e∈E(F) we have e⊂f(e). Berge-F-free it does not contain copies F. We address the saturation problem concerning hypergraphs, i.e. what minimum number satr(n,Berge-F) hyperedges in an r-uniform H with property adding new hyperedge (of size r) to creates F? prove grows linearly n F either complete multipartite or possesses following property: d1≤d2≤⋯≤d|V(F)| degree sequence then contains two adjacent vertices u,v dF(u)=d1, dF(v)=d2. In particular, Berge-saturation regular graphs n.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2022
ISSN: ['1095-9971', '0195-6698']
DOI: https://doi.org/10.1016/j.ejc.2021.103477