Geodesic
Subgraph densities in \(K_r\)-free graphs
Andrzej Grzesik1 ; Ervin Győri2 ; Nika Salia3 ; Casey Tompkins2
1Jagiellonian University
2Alfred Renyi Institute of Mathematics
3Alfréd Rényi Institute of Mathematics
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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In this paper we disprove a conjecture of Lidický and Murphy about the number of copies of a given graph in a $K_r$-free graph and give an alternative general conjecture. We also prove an asymptotically tight bound on the number of copies of any bipartite graph of radius at most~$2$ in a triangle-free graph.
DOI : 10.37236/11329
Classification : 05C35, 05C42
Mots-clés : pentagon density, triangle-free graphs, extremal graph theory

Andrzej Grzesik  1   ; Ervin Győri  2   ; Nika Salia  3   ; Casey Tompkins  2

1 Jagiellonian University
2 Alfred Renyi Institute of Mathematics
3 Alfréd Rényi Institute of Mathematics 
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     title = {Subgraph densities in {\(K_r\)-free} graphs},
     journal = {The electronic journal of combinatorics},
     year = {2023},
     volume = {30},
     number = {1},
     doi = {10.37236/11329},
     zbl = {1511.05112},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11329/}
}
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Andrzej  Grzesik; Ervin  Győri; Nika Salia; Casey Tompkins. Subgraph densities in \(K_r\)-free graphs. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11329

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