Succinct Data Structures for Small Clique-Width Graphs

Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability. In this paper we design a succinct data structure for graphs on $n$ vertices whose clique-width is at most $k \leq \epsilon \sqrt{\log n / \log \log n}$ for some constant $0<\epsilon<1$, along with supporting degree, adjacency, neighborhood queries efficiently. This resolves an open problem of Kamali (Algorithmica-2018).