2022/03/07 by Barnaby Martin, Daniël Paulusma, Martin, Barnaby +5
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Limits and Structures in Graph Theory
paper · doi:10.48550/arxiv.2203.03319
openalex publication_date 2022/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Paths P1,…,Pk in a graph G=(V,E) are mutually induced if any two distinct Pi and Pj have neither common vertices nor adjacent vertices. For a fixed integer k, the k-Induced Disjoint Paths problem is to decide if a graph G with k pairs of specified vertices (si,ti) contains k mutually induced paths Pi such that each Pi starts from si and ends at ti. Whereas the non-induced version is well-known to be polynomial-time solvable for every fixed integer k, a classical result from the literature states that even 2-Induced Disjoint Paths is NP-complete. We prove new complexity results for k-Induced Disjoint Paths if the input is restricted to H-free graphs, that is, graphs without a fixed graph H as an induced subgraph. We compare our results with a complexity dichotomy for Induced Disjoint Paths, the variant where k is part of the input.