%A Blumenthal, Adam %A Lidický, Bernard %A Pikhurko, Oleg %A Pehova, Yanitsa %A Pfender, Florian %A Volec, Jan %D 2019 %T Sharp bounds for decomposing graphs into edges and triangles %K %X Let pi 3 (G) be the minimum of twice the number of edges plus three times the number of triangles over all edge-decompositions of G into copies of K 2 and K 3 . We are interested in the value of pi 3 (n) , the maximum of pi 3 (G) over graphs G with n vertices. This specific extremal function was first studied by Gyori and Tuza [Decompositions of graphs into complete subgraphs of given order, Studia Sci . Math . Hungar . 22 (1987), 315--320], who showed that pi 3 (n)<9n 2 /16 . In a recent advance on this problem, Kral , Lidicky , Martins and Pehova [ arXiv :1710:08486] proved via flag algebras that pi 3 (n)<(1/2+o(1))n 2 , which is tight up to the o(1) term. We extend their proof by giving the exact value of pi 3 (n) for large n , and we show that K n and K n/2,n/2 are the only extremal examples.   %U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1191 %J Acta Mathematica Universitatis Comenianae %0 Journal Article %P 463-468%V 88 %N 3 %@ 0862-9544 %8 2019-07-26