Space-efficient FPT Algorithms for Degeneracy

Abstract

The degeneracy of a graph G is defined as the smallest value k such that every subgraph of G has a vertex with a degree of at most k. Given a graph G, its degeneracy can be easily calculated provided sufficient memory is available. In this paper, we focus on scenarios where only o(n) bits of additional read-write memory are available, apart from the input stored in read-only memory. Within this context, we introduce two FPT algorithms for degeneracy, parameterized by neighborhood diversity and the cluster vertex deletion number.