{"paper":{"title":"Counting Small Induced Subgraphs: Hardness of Symmetry-Based Properties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Mingjun Liu, Radu Curticapean","submitted_at":"2026-06-30T15:21:13Z","abstract_excerpt":"Jerrum and Meeks (TOCT, JCSS 2015) introduced the counting problems $\\text{IndSub}(\\Phi)$ for fixed graph properties $\\Phi$: Given an input graph $G$ and $k\\in\\mathbb N$, count the $k$-vertex subsets $S \\subseteq V(G)$ such that the induced subgraph $G[S]$ satisfies $\\Phi$. For recursively enumerable $\\Phi$, it is known that $\\text{IndSub}(\\Phi)$ is either #W[1]-hard or fixed-parameter tractable. A direct classification depending on $\\Phi$ however still remains open.\n  In particular, the status was open for the property of graphs without nontrivial automorphisms, also mentioned in a very recen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31803","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.31803/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}