Perfect matchings in shadow colorings (Q2220968)

Let \(H\) be a hypergraph on a vertex set \(V.\) Then \(H(G),\) the shadow graph of \(H,\) has the same vertex set, and \(\{x,y\}\) is an edge of \(H(G)\) if there is an hyperedge of \(C\) containing both \(x\) and \(y.\) An edge coloring of \(H\) induces a multicoloring of edges of \(H(G)\) where \(\{x,y\}\) is assigned a color \(c\) if there is an edge of \(H\) covering \(x\) and \(y\) colored by \(c,\).\par Let \(\left\vert V\right\vert \) be even. In this paper, the author proves that any \((r-1)\) edge coloring of the complete \(r\)-uniform hypergraph \(KH_{n}^{r}\) induces a coloring of \(H(G)\) that possesses a monochromatic perfect matching.