Geodesic
Directed graphs without rainbow stars
Dániel Gerbner1 ; Andrzej Grzesik2 ; Cory Palmer3 ; Magdalena Prorok4
1Alfréd Rényi Institute of Mathematics, HUN-REN
2Faculty of Mathematics and Computer Science, Jagiellonian University
3Department of Mathematical Sciences, University of Montana
4AGH University of Krakow
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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In a rainbow version of the classical Turán problem one considers multiple graphs on a common vertex set, thinking of each graph as edges in a distinct color, and wants to determine the minimum number of edges in each color which guarantees existence of a rainbow copy (having at most one edge from each graph) of a given graph. Here, we prove an optimal solution for this problem for any directed star and any number of colors.
DOI : 10.37236/12784
Classification : 05C20, 05C35
Mots-clés : directed star, Turán problem

Dániel Gerbner  1   ; Andrzej Grzesik  2   ; Cory Palmer  3   ; Magdalena Prorok  4

1 Alfréd Rényi Institute of Mathematics, HUN-REN
2 Faculty of Mathematics and Computer Science, Jagiellonian University
3 Department of Mathematical Sciences, University of Montana
4 AGH University of Krakow 
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     author = {D\'aniel Gerbner and Andrzej Grzesik and Cory Palmer and Magdalena Prorok},
     title = {Directed graphs without rainbow stars},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {4},
     doi = {10.37236/12784},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/12784/}
}
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Dániel Gerbner; Andrzej Grzesik; Cory Palmer; Magdalena Prorok. Directed graphs without rainbow stars. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12784

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