Claims
Search the graph by meaning. Each result carries its current verdict; open one to see its decomposition, provenance, and the reasoning behind the assessment.
KindShowingImportancePrizesTopicGraph theory
The study of graphs — vertices, edges, connectivity, coloring, planarity, and extremal or random graph problems. Claims about graph-theoretic theorems, conjectures, and open problems belong here.
Erdős's unit distance problem is equivalent to finding the maximum number of edges of a unit-distance graph on n vertices.
VerifiedThe evidence, examined directly, establishes the claim.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Erdős unit distance conjectureDiscrete geometryimportance · settledImportance 0.10, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Every graph with n vertices and m ≥ 4n edges has crossing number Ω(m^3/n^2).
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Crossing lemmaimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
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