Two graphs G and H are hypomorphic if there exists a bijection φ: V (G)→ V (H) such that G−
v≅ H− φ (v) for each v∈ V (G). A graph G is reconstructible if H≅ G for all H hypomorphic to …

The $\ell $-deck of a graph $ G $ is the multiset of all induced subgraphs of $ G $ on $\ell $
vertices. We say that a graph is reconstructible from its $\ell $-deck if no other graph has the …

This thesis explores the difficulties of capturing graph structure, and the recent approaches
that have been able to do so effectively in some settings. The famous Graph Reconstruction …

This thesis work deals with the problem of learning the topology of a network starting from
the signals emitted by the network nodes while executing some distributed processing task …

A classical notion in graph theory is that of the block-cut vertex tree of a graph. It tells us that
if we consider the maximal 2-connected components of a connected graph G then they are …

A simple graph is given by a set of vertices V and a set of edges E, where each element of E
consists of two distinct elements of V. We do not allow self-loops or multiple edges between …

It is a long-standing problem in graph theory to prove or disprove the reconstruction
conjecture, also known as the Kelly-Ulam conjecture. This conjecture states that every …

We say that two graphs G and H are (vertex-) hypomorphic if there exists a bijection ϕ
between the vertices of G and H such that the induced subgraphs G− v and H− ϕ (v) are …

We begin with a brief introduction to the chromatic and Tutte polynomial of graphs. We then
give an introduction to Hopf algebras. In combinatorics, Hopf algebras arise since many …

Nous livrons d'abord un prolongement et une mise à jour de l'article [10] en explorant de
nouvelles propriétés des chaînes insécables. Nous montrons la Halin-reconstructibilité des …