The $(\leq 6)$-half-reconstructibility of digraphs

Abstract

Let $G=(V,A)$ be a digraph. With every subset $X$ of $V$, we associate the subdigraph $G[X]=(X,A\cap (X\times X))$ of $G$ induced by $X$. Given a positive integer $k$, a digraph $G$ is $(\leq k)$-half-reconstructible if it is determined up to duality by its subdigraphs of cardinality $\leq k$. In 2003, J. Dammak characterized the $(\leq k)$-half-reconstructible finite digraphs, for $k\in \{7,8,9,10,11\}$. N. El Amri, extended J. Dammak's characterization to infinite digraphs. In this paper, we characterize the $(\leq 6)$-half-reconstructible infinite digraphs.