TR-2013-02

Splitting property via shadow systems

Kristóf Bérczi, Péter Csikvári, Erika Renáta Bérczi-Kovács, László Végh

Let $M_k^r$ denote the set of $r$-element multisets over the set $\{1,\dots,k\}$. We show that $M_k^k$ has the so-called splitting property introduced by Ahlswede et al. Our approach gives a new interpretation of Sidorenko's construction and is applicable to give an upper bound on weighted Turán numbers, matching previous bounds. We also show how these results are connected to Tuza's conjecture on minimum triangle covers.

Bibtex entry:

@techreport{egres-13-02,

AUTHOR	=	{B{\'e}rczi, Krist{\'o}f and Csikv{\'a}ri, P{\'e}ter and B{\'e}rczi-Kov{\'a}cs Ren{\'a}ta, Erika and V{\'e}gh, L{\'a}szl{\'o}},
TITLE	=	{Splitting property via shadow systems},
NOTE	=	{{\tt egres.elte.hu}},
INSTITUTION	=	{Egerv{\'a}ry Research Group, Budapest},
YEAR	=	{2013},
NUMBER	=	{TR-2013-02}

}