Sharp bounds for decomposing graphs into edges and triangles

  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},
  • Adam Blumenthal, B. Lidický, +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
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