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

Baraa Salem, Jamel Dammak

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.

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

Abstract

Let be a digraph. With every subset of , we associate the subdigraph of induced by . Given a positive integer , a digraph is -half-reconstructible if it is determined up to duality by its subdigraphs of cardinality . In 2003, J. Dammak characterized the -half-reconstructible finite digraphs, for . N. El Amri, extended J. Dammak's characterization to infinite digraphs. In this paper, we characterize the -half-reconstructible infinite digraphs.

Paper Structure

This paper contains 3 sections, 2 figures.

Table of Contents

  1. Introduction
  2. The $(\leq 6)$-half-reconstructibility of arc-connected digraphs
  3. Proof of Theorem \ref{['T1']}.

Figures (2)

  • Figure 1: Flag and peaks.
  • Figure 2: Diamond, $3$-consecutivity, $3$-cycle.