Geodesic
Edge ordered Turán problems
Dániel Gerbner1 ; Abhishek Methuku2 ; Dániel T. Nagy1 ; Dömötör Pálvölgyi3 ; Gábor Tardos1 ; Máté Vizer1 ; Dániel Gerbner ; Abhishek Methuku ; Dániel T. Nagy ; Dömötör Pálvölgyi ; Gábor Tardos ; Máté Vizer
1Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary
2École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland and Central European University, Budapest, Hungary
3MTA-ELTE Lendület Combinatorial Geometry Research Group, Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 717-722 
Dániel Gerbner; Abhishek Methuku; Dániel T. Nagy; Dömötör Pálvölgyi; Gábor Tardos; Máté Vizer; Dániel Gerbner; Abhishek Methuku; Dániel T. Nagy; Dömötör Pálvölgyi; Gábor Tardos; Máté Vizer. Edge ordered Turán problems. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 717-722. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a55/
@article{AMUC_2019_88_3_a55,
     author = {D\'aniel Gerbner and Abhishek Methuku and D\'aniel T. Nagy and D\"om\"ot\"or P\'alv\"olgyi and G\'abor Tardos and M\'at\'e Vizer and D\'aniel Gerbner and Abhishek Methuku and D\'aniel T. Nagy and D\"om\"ot\"or P\'alv\"olgyi and G\'abor Tardos and M\'at\'e Vizer},
     title = { Edge ordered {Tur\'an} problems},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {717--722},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a55/}
}
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AU  - Gábor Tardos
AU  - Máté Vizer
AU  - Dániel Gerbner
AU  - Abhishek Methuku
AU  - Dániel T. Nagy
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AU  - Gábor Tardos
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JO  - Acta mathematica Universitatis Comenianae
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%A Dömötör Pálvölgyi
%A Gábor Tardos
%A Máté Vizer
%A Dániel Gerbner
%A Abhishek Methuku
%A Dániel T. Nagy
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%A Gábor Tardos
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%F AMUC_2019_88_3_a55

Voir la notice de l'article provenant de la source Comenius University

We introduce the Tur\'an problem for edge ordered graphs. We call a simple graph \emph{edge ordered}, if its edges are linearly ordered. An isomorphism between edge ordered graphs must respect the edge order. A subgraph of an edge ordered graph is itself an edge ordered graph with the induced edge order. We say that an edge ordered graph $G$ \emph{avoids} another edge ordered graph $H$, if no subgraph of $G$ is isomorphic to $H$. The Tur\'an number $\mathrm{ex}'_{<}(n,\mathcal{H})$ of a family $\mathcal{H}$ of edge ordered graphs is the maximum number of edges in an edge ordered graph on $n$ vertices that avoids all elements of $\mathcal{H}$. We examine this parameter in general and also for several singleton families of edge orders of certain small specific graphs, like star forests, short paths and the cycle of length four.