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.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
A bull-free graph
Definition
A finite simple graph is bull-free when it has no induced copy of the bull graph (The bull graph). Equivalently, is bull-free in the sense of the general induced-subgraph convention of -free and -free graphs under the induced-subgraph convention.
Depends on
Used by
- The five-cycle is bull-free but not perfect Counterexample
- A split set in a bull-free graph Definition
- Basic and composite bull-free graphs Definition
- K₄ is bull-free and has a nontrivial module Example
- A graph is bull-free if and only if its complement is bull-free Proposition
- A split set with both a complete and an anticomplete outside vertex yields a nontrivial module Theorem
Dependency tree · two levels
5 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
- Maria Chudnovsky and Shmuel Safra, The Erdős-Hajnal conjecture for bull-free graphs, Section 1 (standard reference, not scraped)