Finite 3-set-homogeneous graphs

Zhou, Jin‐Xin

doi:10.1016/j.ejc.2020.103275

Cited by 5 publications

(2 citation statements)

References 36 publications

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“…Enomoto's argument was shown in [26, Lemma 3.1] to work for finite tournaments, but not for finite digraphs (a directed 5‐cycle is set‐homogeneous but not homogeneous). Finite set‐homogeneous directed graphs (allowing pairs with an arc in each direction) were classified in [26], and [42] initiated an analysis of finite 3‐set‐homogeneous graphs.…”

Section: Introductionmentioning

confidence: 99%

Set‐homogeneous hypergraphs

Assari

Hosseinzadeh

Macpherson

2023

Journal of London Math Soc

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A ‐uniform hypergraph is set‐homogeneous if it is countable (possibly finite) and whenever two finite induced subhypergraphs are isomorphic there is with ; the hypergraph is said to be homogeneous if in addition every isomorphism between finite induced subhypergraphs extends to an automorphism. We give four examples of countably infinite set‐homogeneous ‐uniform hypergraphs that are not homogeneous (two with , one with and one with ). Evidence is also given that these may be the only ones, up to complementation. For example, for there is just one countably infinite ‐uniform hypergraph whose automorphism group is not 2‐transitive, and there is none for . We also give an example of a finite set‐homogeneous 3‐uniform hypergraph that is not homogeneous.

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Section: Introductionmentioning

confidence: 99%

Set‐homogeneous hypergraphs

Assari

Hosseinzadeh

Macpherson

2023

Journal of London Math Soc

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“…Enomoto's argument was shown in [25,Lemma 3.1] to work for finite tournaments, but not for finite digraphs (a directed 5-cycle is sethomogeneous but not homogeneous). Finite set-homogeneous directed graphs (allowing pairs with an arc in each direction) were classified in [25], and [40] initiates an analysis of finite 3-set-homogeneous graphs.…”

Section: Introduction 1backgroundmentioning

confidence: 99%

Set-homogeneous hypergraphs

Assari¹,

Hosseinzadeh²,

Macpherson³

2022

Preprint

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A k-uniform hypergraph M is set-homogeneous if it is countable (possibly finite) and whenever two finite induced subhypergraphs U, V are isomorphic there is g ∈ Aut(M ) with U g = V ; the hypergraph M is said to be homogeneous if in addition every isomorphism between finite induced subhypergraphs extends to an automorphism. We give four examples of countably infinite set-homogeneous k-uniform hypergraphs which are not homogeneous (two with k = 3, one with k = 4, and one with k = 6). Evidence is also given that these may be the only ones, up to complementation. For example, for k = 3 there is just one countably infinite k-uniform hypergraph whose automorphism group is not 2-transitive, and there is none for k = 4. We also give an example of a finite set-homogeneous 3-uniform hypergraph which is not homogeneous.

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Finite 4-geodesic-transitive graphs with bounded girth

Jin,

Tan

2024

J Algebr Comb

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Finite 3-set-homogeneous graphs

Cited by 5 publications

References 36 publications

Set‐homogeneous hypergraphs

Set‐homogeneous hypergraphs

Set-homogeneous hypergraphs

Finite 4-geodesic-transitive graphs with bounded girth

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