{"paper":{"title":"The Maximum Degree-and-Diameter-Bounded Subgraph in the Mesh","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Hebert Perez-Roses, Joe Ryan, Mirka Miller","submitted_at":"2012-03-19T10:01:50Z","abstract_excerpt":"The problem of finding the largest connected subgraph of a given undirected host graph, subject to constraints on the maximum degree $\\Delta$ and the diameter $D$, was introduced in \\cite{maxddbs}, as a generalization of the Degree-Diameter Problem. A case of special interest is when the host graph is a common parallel architecture. Here we discuss the case when the host graph is a $k$-dimensional mesh. We provide some general bounds for the order of the largest subgraph in arbitrary dimension $k$, and for the particular cases of $k=3, \\Delta = 4$ and $k=2, \\Delta = 3$, we give constructions t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4069","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"}