Modular Decomposition and the Reconstruction Conjecture

TL;DR

This paper proves that a broad class of graphs, decomposable via modular decomposition, can be reconstructed solely from their vertex-deleted subgraphs, advancing understanding of graph reconstructibility.

Contribution

It establishes that graphs decomposable by modular decomposition are reconstructible from their vertex-deleted subgraphs, expanding the class of reconstructible graphs.

Findings

Large family of modular decomposable graphs are reconstructible

Reconstruction from vertex-deleted subgraphs is possible for these graphs

Advances the graph reconstruction conjecture for a new class

Abstract

We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.