On the recognition algorithm of edge intersection graphs of linear $3$-uniform hypergraphs: prelarge cliques

Let $L^l_k$ be the class of edge intersection graphs of linear $k$-uniform hypergraphs. It is known that the recognition problem "$G\in L^l_k$" is $NP$-complete for $k\ge 3$, but there exists an algorithm deciding whether $G\in L^l_3$ for graphs $G$ with minimal vertex degree $\delta(G)\ge 10$. In this paper we provide the practical oriented modification of this algorithm.