# Sharp bounds for decomposing graphs into edges and triangles

@article{Blumenthal2019SharpBF,
title={Sharp bounds for decomposing graphs into edges and triangles},
author={Adam Blumenthal and B. Lidick{\'y} and Yanitsa Pehova and Florian Pfender and O. Pikhurko and J. Volec},
journal={Combinatorics, Probability & Computing},
year={2019},
pages={1-17}
}
• Adam Blumenthal, +3 authors J. Volec
• Published 2019
• Mathematics
• Combinatorics, Probability & Computing
• For a real constant $\alpha$, let $\pi_3^\alpha(G)$ be the minimum of twice the number of $K_2$'s plus $\alpha$ times the number of $K_3$'s over all edge decompositions of $G$ into copies of $K_2$ and $K_3$, where $K_r$ denotes the complete graph on $r$ vertices. Let $\pi_3^\alpha(n)$ be the maximum of $\pi_3^\alpha(G)$ over all graphs $G$ with $n$ vertices. The extremal function $\pi_3^3(n)$ was first studied by Győri and Tuza [Decompositions of graphs into complete subgraphs of given order… CONTINUE READING
2 Citations

#### References

SHOWING 1-10 OF 43 REFERENCES
Edge-decompositions of graphs with high minimum degree
• Mathematics, Computer Science
• Electron. Notes Discret. Math.
• 2015
• 46
• PDF
Decomposing Graphs into Edges and Triangles
• Mathematics, Computer Science
• Comb. Probab. Comput.
• 2019
• 4
• PDF
On the Minimal Density of Triangles in Graphs
• A. Razborov
• Mathematics, Computer Science
• Comb. Probab. Comput.
• 2008
• 122
• Highly Influential
Progress towards Nash-Williams' conjecture on triangle decompositions
• Mathematics, Computer Science
• J. Comb. Theory, Ser. B
• 2021
• 8
• Highly Influential
• PDF
Fractional Triangle Decompositions in Graphs with Large Minimum Degree
• F. Dross
• Mathematics, Computer Science
• SIAM J. Discret. Math.
• 2016
• 32
• Highly Influential
• PDF
On the Minimum Degree Required for a Triangle Decomposition
• Mathematics, Computer Science
• SIAM J. Discret. Math.
• 2020
• 4
• Highly Influential
• PDF
A problem of Erdős on the minimum number of k-cliques
• Mathematics, Computer Science
• J. Comb. Theory, Ser. B
• 2013
• 29
• PDF