Maximizing five-cycles in Kr-free graphs

@article{Lidick2021MaximizingFI,
  title={Maximizing five-cycles in Kr-free graphs},
  author={Bernard Lidick{\'y} and Kyle Murphy},
  journal={Eur. J. Comb.},
  year={2021},
  volume={97},
  pages={103367}
}

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References

SHOWING 1-10 OF 44 REFERENCES
Minimizing the number of 5-cycles in graphs with given edge-density
TLDR
It is shown that every graph of order n and size, where k ≥ 3 is an integer, contains at least at least two copies of C5, the minimal density of the 5-cycle C 5.
A problem of Erdős and Sós on 3-graphs
AbstractWe show that for every ɛ > 0 there exist δ > 0 and n0 ∈ ℕ such that every 3-uniform hypergraph on n ≥ n0 vertices with the property that every k-vertex subset, where k ≥ δn, induces at least
Sharp bounds for decomposing graphs into edges and triangles
TLDR
Král’, Lidický, Martins and Pehova proved via flag algebras that Kn and the complete bipartite graph ${K_{\lfloor n/2 \rfloor,\lceil n/ 2 \rceil }} are the only possible extremal examples for large n.
The minimum size of 3-graphs without a 4-set spanning no or exactly three edges
On the maximal number of certain subgraphs inKr-free graphs
TLDR
It is shown that in the class of allKr-free graphs withn vertices the complete balanced (r − 1)-partite graphTr−1(n) has the largest number of subgraphs isomorphic toKt (t < r),C4,K2,3.
Applications of the Semi-Definite Method to the Turán Density Problem for 3-Graphs
TLDR
Flagmatic, an implementation of Razborov's semi-definite method, is made publicly available, and several new constructions, conjectures and bounds for Turán densities of 3-graphs which should be of interest to researchers in the area are given.
Supersaturation for Subgraph Counts
The classical extremal problem is that of computing the maximum number of edges in an F -free graph. In particular, Turán’s theorem entirely resolves the case where $$F=K_{r+1}$$ F = K r + 1 . Later
On the number of pentagons in triangle-free graphs
Pentagons in triangle-free graphs
Counting copies of a fixed subgraph in F-free graphs
...
...