The Complexity of Mixed-Connectivity

TL;DR

This paper explores the computational complexity of disconnecting a graph by removing a specified number of vertices and edges, focusing on parameterized complexity for various graph disconnection problems.

Contribution

It introduces a detailed analysis of the parameterized complexity of mixed-connection problems involving vertex and edge removals.

Findings

Complexity results for disconnecting graphs with vertex and edge removals.

Identification of fixed-parameter tractability in certain cases.

Hardness results for other parameter combinations.

Abstract

We investigate the parameterized complexity in $a$ and $b$ of determining whether a graph~$G$ has a subset of $a$ vertices and $b$ edges whose removal disconnects $G$, or disconnects two prescribed vertices $s, t \in V(G)$.