{"paper":{"title":"Boxicity of Line Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"L. Sunil Chandran, Naveen Sivadasan, Rogers Mathew","submitted_at":"2010-09-22T20:24:06Z","abstract_excerpt":"Boxicity of a graph H, denoted by box(H), is the minimum integer k such that H is an intersection graph of axis-parallel k-dimensional boxes in R^k. In this paper, we show that for a line graph G of a multigraph, box(G) <= 2\\Delta(\\lceil log_2(log_2(\\Delta)) \\rceil + 3) + 1, where \\Delta denotes the maximum degree of G. Since \\Delta <= 2(\\chi - 1), for any line graph G with chromatic number \\chi, box(G) = O(\\chi log_2(log_2(\\chi))). For the d-dimensional hypercube H_d, we prove that box(H_d) >= (\\lceil log_2(log_2(d)) \\rceil + 1)/2. The question of finding a non-trivial lower bound for box(H_d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4471","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"}