{"paper":{"title":"$E$-restricted double traces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Archdeacon, Jernej Rus, Luis Goddyn","submitted_at":"2016-10-31T12:13:10Z","abstract_excerpt":"For a graph $G$ and $E \\subseteq E(G)$, $E$-restricted strong trace is a closed walk which traverses every edge from $E$ once in each direction and every other edge twice in the same direction. In addition, every time a strong trace come to a vertex $v$ from $N \\subseteq N(v)$ it continues to $u \\notin N$, for $1 \\leq |N| < d(v)$. We characterize graphs admitting $E$-restricted strong traces and explain how this result can be used as an upgrade of mathematical model for self-assembling nanostructure design first presented by Gradi\\v{s}ar et al. in [Design of a single-chain polypeptide tetrahed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09888","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"}