{"paper":{"title":"Zero forcing for inertia sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"H. Tracy Hall, Jason Grout, Steve Butler","submitted_at":"2012-11-19T22:53:10Z","abstract_excerpt":"Zero forcing is a combinatorial game played on a graph with a goal of turning all of the vertices of the graph black while having to use as few \"unforced\" moves as possible. This leads to a parameter known as the zero forcing number which can be used to give an upper bound for the maximum nullity of a matrix associated with the graph.\n  We introduce a new variation on the zero forcing game which can be used to give an upper bound for the maximum nullity of a matrix associated with a graph that has $q$ negative eigenvalues. This gives some limits to the number of positive eigenvalues that such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4618","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":""},"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"}