Geodesic
Crowns in linear \(3\)-graphs of minimum degree \(4\)
Alvaro Carbonero1 ; Willem Fletcher2 ; Jing Guo3 ; András Gyárfás4 ; Rona Wang5 ; Shiyu Yan6
1University of Waterloo
2Carleton College
3University of Utah
4Alfréd Rényi Institute of Mathematics
5Massachusetts Institute of Technology
6University of Cambridge
The electronic journal of combinatorics, Tome 29 (2022) no. 4
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A 3-graph is a pair H = (V, E) of sets, where elements of V are called points or vertices and E contains some 3-element subsets of V , called edges. A 3-graph is called linear if any two distinct edges intersect in at most one vertex.There is a recent interest in extremal properties of 3-graphs containing no crown, three pairwise disjoint edges and a fourth edge which intersects all of them. We show that every linear 3-graph with minimum degree 4 contains a crown. This is not true if 4 is replaced by 3.
DOI : 10.37236/11037
Classification : 05C35, 05B07, 05D05, 05C30
Mots-clés : Steiner triple systems, Turán number

Alvaro Carbonero  1   ; Willem Fletcher  2   ; Jing Guo  3   ; András Gyárfás  4   ; Rona Wang  5   ; Shiyu Yan  6

1 University of Waterloo
2 Carleton College
3 University of Utah
4 Alfréd Rényi Institute of Mathematics
5 Massachusetts Institute of Technology
6 University of Cambridge 
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     title = {Crowns in linear \(3\)-graphs of minimum degree \(4\)},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {4},
     doi = {10.37236/11037},
     zbl = {1503.05065},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11037/}
}
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Alvaro Carbonero; Willem Fletcher; Jing Guo; András Gyárfás; Rona Wang; Shiyu Yan. Crowns in linear \(3\)-graphs of minimum degree \(4\). The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/11037

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