2021/10/29 by Ajinkya Gaikwad, Gaikwad, Ajinkya, Soumen Maity +1
Computer Science · #Advanced Graph Theory Research #Artificial Intelligence (cs.AI) #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Formal Methods in Verification
paper · pdf · doi:10.48550/arxiv.2110.15757
openalex publication_date 2021/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Offensive Alliance problem has been studied extensively during the last twenty years. A set S⊆ V of vertices is an offensive alliance in an undirected graph G=(V,E) if each v∈ N(S) has at least as many neighbours in S as it has neighbours (including itself) not in S. We study the parameterized complexity of the Offensive Alliance problem, where the aim is to find a minimum size offensive alliance. Our focus here lies on parameters that measure the structural properties of the input instance. We enhance our understanding of the problem from the viewpoint of parameterized complexity by showing that the problem is W[1]-hard parameterized by a wide range of fairly restrictive structural parameters such as the feedback vertex set number, treewidth, pathwidth, and treedepth of the input graph.