Z_2× Z_2-cordial cycle-free hypergraphs

Hovey introduced $A$-cordial labelings as a generalization of cordial and harmonious \cite{Hovey}. If $A$ is an Abelian group, then labeling $f \colon V (G) \rightarrow A$ the vertices some graph $G$ induces edge on $G$, $uv$ receives label (u) + f (v)$. A if there vertex-labeling such that (1) vertex classes differ in size by at most one (2) induced one. The problem graphs can be naturally extended for hypergraphs. It was shown not every $2$-uniform hypertree (i.e., tree) admits $Z_2\times Z_2$-cordial \cite{Pechnik}. situation changes we consider $p$-uniform hypetrees bigger $p$. We prove any $p>2$, so path hypergraph which all edges have least~3. property valid universally class hypergraphs maximum degree~1, provide necessary sufficient condition.