Let $G$ be a cancellative $3$-uniform hypergraph in which the symmetric difference of any two edges is not contained in a third one. Equivalently, a $3$-uniform hypergraph $G$ is cancellative if and only if $G$ is $\{F_4, F_5\}$-free, where $F_4 = \{abc, abd, bcd\}$ and $F_5 = \{abc, abd, cde\}$. A classical result in extremal combinatorics stated that the maximum size of a cancellative hypergraph is achieved by the balanced complete tripartite $3$-uniform hypergraph, which was firstly proved by Bollobás and later by Keevash and Mubayi. In this paper, we consider spectral extremal problems for cancellative hypergraphs. More precisely, we determine the maximum $p$-spectral radius of cancellative $3$-uniform hypergraphs, and characterize the extremal hypergraph. As a by-product, we give an alternative proof of Bollobás' result from spectral viewpoint.
@article{10_37236_12345,
author = {Zhenyu Ni and Lele Liu and Liying Kang},
title = {Spectral {Tur\'an-type} problems on cancellative hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {2},
doi = {10.37236/12345},
zbl = {1543.05117},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12345/}
}
TY - JOUR
AU - Zhenyu Ni
AU - Lele Liu
AU - Liying Kang
TI - Spectral Turán-type problems on cancellative hypergraphs
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/12345/
DO - 10.37236/12345
ID - 10_37236_12345
ER -
%0 Journal Article
%A Zhenyu Ni
%A Lele Liu
%A Liying Kang
%T Spectral Turán-type problems on cancellative hypergraphs
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/12345/
%R 10.37236/12345
%F 10_37236_12345
Zhenyu Ni; Lele Liu; Liying Kang. Spectral Turán-type problems on cancellative hypergraphs. The electronic journal of combinatorics, Tome 31 (2024) no. 2. doi: 10.37236/12345
