2026-07-25T05:30:25Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18120 2024-03-06T11:01:04Z ddc:004 open_access

Parameterised and Fine-Grained Subgraph Counting, Modulo 2 Goldberg, Leslie Ann Roth, Marc modular counting parameterised complexity fine-grained complexity subgraph counting Given a class of graphs ℋ, the problem ⊕Sub(ℋ) is defined as follows. The input is a graph H ∈ ℋ together with an arbitrary graph G. The problem is to compute, modulo 2, the number of subgraphs of G that are isomorphic to H. The goal of this research is to determine for which classes ℋ the problem ⊕Sub(ℋ) is fixed-parameter tractable (FPT), i.e., solvable in time f(|H|)⋅|G|^O(1). Curticapean, Dell, and Husfeldt (ESA 2021) conjectured that ⊕Sub(ℋ) is FPT if and only if the class of allowed patterns ℋ is matching splittable, which means that for some fixed B, every H ∈ ℋ can be turned into a matching (a graph in which every vertex has degree at most 1) by removing at most B vertices. Assuming the randomised Exponential Time Hypothesis, we prove their conjecture for (I) all hereditary pattern classes ℋ, and (II) all tree pattern classes, i.e., all classes ℋ such that every H ∈ ℋ is a tree. We also establish almost tight fine-grained upper and lower bounds for the case of hereditary patterns (I). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Leslie Ann Goldberg and Marc Roth 2023 Is Part Of LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2023.68 urn:nbn:de:0030-drops-181200 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.68 eng https://creativecommons.org/licenses/by/4.0/legalcode