# Articles by Hugo Demaret

## Fractional domatic number and minimum degree

summary: We present a study of a graph parameter in graph theory, named the fractional domatic number. A dominating set in a graph is a set of vertices such that every vertex outside the set is adjacent to a vertex in the set. The domatic number of a graph is ...

## Compact local certification of MSO properties for several tree-like parameters

summary: Local certification is interested in assigning labels (called certificates) to the vertices of a graph, in order to certify a certain property about said graph, or the correctness of a data-structure distributed on the graph. For the verification to be local, a vertex may only "see" its neighbourhood. A ...