If, in a simple graph on n vertices with n at least three, every pair of non-adjacent vertices has degrees summing to at least n, the graph contains a Hamiltonian cycle. Proved by Oystein Ore, it strengthens Dirac's earlier minimum-degree condition for Hamiltonicity.
Facts
StatementIf, in a finite simple graph with n greater than or equal to 3 vertices, every pair of non-adjacent vertices has degrees summing to at least n, then the graph is Hamiltonian. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Ore's Theorem (Wikipedia)
Wikimedia FoundationLead section
the theorem considers the sum of the degrees of pairs of non-adjacent vertices: if every such pair has a sum that at least equals the total number of vertices in the graph, then the graph is Hamiltonian.
Lead section, proof year
Ore's theorem is a result in graph theory proved in 1960 by Norwegian mathematician Øystein Ore.
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