{"paper":{"title":"Frustrated Triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gabor Meszaros, Teeradej Kittipassorn","submitted_at":"2014-11-06T20:58:35Z","abstract_excerpt":"A triple of vertices in a graph is a \\emph{frustrated triangle} if it induces an odd number of edges. We study the set $F_n\\subset[0,\\binom{n}{3}]$ of possible number of frustrated triangles $f(G)$ in a graph $G$ on $n$ vertices. We prove that about two thirds of the numbers in $[0,n^{3/2}]$ cannot appear in $F_n$, and we characterise the graphs $G$ with $f(G)\\in[0,n^{3/2}]$. More precisely, our main result is that, for each $n\\geq 3$, $F_n$ contains two interlacing sequences $0=a_0\\leq b_0\\leq a_1\\leq b_1\\leq \\dots \\leq a_m\\leq b_m\\sim n^{3/2}$ such that $F_n\\cap(b_t,a_{t+1})=\\emptyset$ for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1749","kind":"arxiv","version":2},"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"}