On the sizes of $(k,l)$-edge-maximal $r$-uniform hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 1, pp. 179-194
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Let H=(V,E) be a hypergraph, where V is a set of vertices and E is a set of non-empty subsets of V called edges. If all edges of H have the same cardinality r, then H is an r-uniform hypergraph; if E consists of all r-subsets of V, then H is a complete r-uniform hypergraph, denoted by K_n^r, where n=|V|. An r-uniform hypergraph H=(V,E) is (k,l)-edge-maximal if every subhypergraph H^' of H with |V(H^')|≥ l has edge-connectivity at most k, but for any edge e∈ E(K_n^r)∖ E(H), H+e contains at least one subhypergraph H^” with |V(H^”)|≥ l and edge-connectivity at least k+1. In this paper, we obtain the lower bounds and the upper bounds of the sizes of (k,l)-edge-maximal hypergraphs. Furthermore, we show that these bounds are best possible.
Keywords:
edge-connectivity, $(k,l)$-edge-maximal hypergraphs, $r$-uniform hypergraphs
@article{DMGT_2023_43_1_a11,
author = {Tian, Yingzhi and Lai, Hong-Jian and Meng, Jixiang and Xu, Murong},
title = {On the sizes of $(k,l)$-edge-maximal $r$-uniform hypergraphs},
journal = {Discussiones Mathematicae. Graph Theory},
pages = {179--194},
publisher = {mathdoc},
volume = {43},
number = {1},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGT_2023_43_1_a11/}
}
TY - JOUR AU - Tian, Yingzhi AU - Lai, Hong-Jian AU - Meng, Jixiang AU - Xu, Murong TI - On the sizes of $(k,l)$-edge-maximal $r$-uniform hypergraphs JO - Discussiones Mathematicae. Graph Theory PY - 2023 SP - 179 EP - 194 VL - 43 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGT_2023_43_1_a11/ LA - en ID - DMGT_2023_43_1_a11 ER -
%0 Journal Article %A Tian, Yingzhi %A Lai, Hong-Jian %A Meng, Jixiang %A Xu, Murong %T On the sizes of $(k,l)$-edge-maximal $r$-uniform hypergraphs %J Discussiones Mathematicae. Graph Theory %D 2023 %P 179-194 %V 43 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMGT_2023_43_1_a11/ %G en %F DMGT_2023_43_1_a11
Tian, Yingzhi; Lai, Hong-Jian; Meng, Jixiang; Xu, Murong. On the sizes of $(k,l)$-edge-maximal $r$-uniform hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 1, pp. 179-194. http://geodesic.mathdoc.fr/item/DMGT_2023_43_1_a11/