Computing Tree-depth Faster Than $2^n$

Abstract

A connected graph has tree-depth at most $k$ if it is a subgraph of the closure of a rooted tree whose height is at most $k$. We give an algorithm which for a given $n$-vertex graph $G$, in time $\mathcal{O}(1.9602^n)$ computes the tree-depth of $G$. Our algorithm is based on combinatorial results revealing the structure of minimal rooted trees whose closures contain $G$.

References in corpus (1)

• Determinant Sums for Undirected Hamiltonicity

Cited by in corpus (1)

• SAT-Encodings for Treecut Width and Treedepth