Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
The right six-vertex prime -graph
Definition
The right six-vertex prime -graph is the complement of the left six-vertex prime -graph on the same labelled vertex set (The left six-vertex prime -graph, Graph isomorphisms, automorphisms and graph complements). Explicitly, its edges are The degrees in the order are .
This complement is isomorphic to the right drawing in Nguyen–Scott–Seymour, Figure 1; the shared labels here are inherited from the left graph and are not the positions in the right drawing.
Remarks
The earlier interpretation as the complement of the triangle-with-three-leaves net is superseded together with the corrected left-graph definition.
Depends on
Used by
Dependency tree · two levels
4 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Tung Nguyen, Alex Scott, and Paul Seymour, Induced subgraph density. IV. New graphs with the Erdős-Hajnal property, Figure 1 (standard reference, not scraped)
- Shenwei Huang, Yiao Ju, and Yidong Zhou, Erdős-Hajnal beyond the five-vertex path, Figure 2 (standard reference, not scraped)