{"paper":{"title":"The Minimum Number of Dependent Arcs and a Related Parameter of Generalized Mycielski Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hsin-Hao Lai, Ko-Wei Lih","submitted_at":"2012-02-29T07:00:02Z","abstract_excerpt":"Let D be an acyclic orientation of the graph G. An arc of D is dependent if its reversal creates a directed cycle. Let m(G) denote the minimum number of dependent arcs over all acyclic orientations of G. For any k > 0, a generalized Mycielski graph M_k(G) of G is defined. Note that M_1(G) is the usual Mycielskian of G. We generalize results concerning m(M_1(G)) in K. L. Collins, K. Tysdal, J. Graph Theory, 46 (2004), 285-296, to m(M_k(G)). The underlying graph of a Hasse diagram is called a cover graph. Let c(G) denote the the minimum number of edges to be deleted from a graph G to get a cover"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6461","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"}