4 Citations
Paths of Length Three are $K_{r+1}$-Turán-Good
- MathematicsElectron. J. Comb.
- 2021
The generalized Turán problem ex$(n,T,F)$ is to determine the maximal number of copies of a graph $T$ that can exist in an $F$-free graph on $n$ vertices. Recently, Gerbner and Palmer noted that the…
Subgraph densities in $K_r$-free graphs
- Mathematics
- 2022
In this paper we disprove a conjecture of Lidick´y 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…
Some stability and exact results in generalized Tur\'an problems
- Mathematics
- 2022
Given graphs H and F , the generalized Tur´an number ex( n, H, F ) is the largest number of copies of H in n -vertex F -free graphs. Stability refers to the usual phenomenon that if an n -vertex F…
Supersaturation for Subgraph Counts
- MathematicsGraphs Comb.
- 2022
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…
References
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Minimizing the number of 5-cycles in graphs with given edge-density
- Mathematics, Computer ScienceCombinatorics, Probability and Computing
- 2019
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
- Mathematics
- 2013
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
- MathematicsCombinatorics, Probability and Computing
- 2020
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
- MathematicsEur. J. Comb.
- 2011
On the maximal number of certain subgraphs inKr-free graphs
- MathematicsGraphs Comb.
- 1991
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
- MathematicsCombinatorics, Probability and Computing
- 2012
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
- MathematicsGraphs Comb.
- 2022
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
- MathematicsJ. Comb. Theory, Ser. A
- 2013