The maximum size of a non-trivial intersecting uniform family that is not a subfamily of the Hilton--Milner family
By Jie Han, Yoshiharu Kohayakawa. 2015
56 citations recorded by the source corpus.
The celebrated Erdős-Ko-Rado theorem determines the maximum size of a $k$-uniform intersecting family. The Hilton-Milner theorem determines the maximum size of a $k$-uniform intersecting family that is not a subfamily of the so-called Erdős-Ko-Rado family. In turn, it is natural to ask what the maximum size of an intersecting $k$-uniform family that is neither a subfamily of the Erdős-Ko-Rado family nor of the Hilton-Milner family is. For $k\ge 4$, this was solved (implicitly) in the same paper by Hilton-Milner in 1967. We give a different and simpler proof, based on the shifting method, which allows us to solve all cases $k\ge 3$ and characterize all extremal families achieving the extremal value.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/732e19ef7691b7ea4d7f0e9de304318dce01fccc
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The structure of large intersecting families (2016, methodology): “Han and Ko-hayakawa [14] refined Theorem 2 using the following construction.”