DefinitionDefinition: AI-adaptedProof: Not applicableaudited 2026-08-27

How 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.

Sparse orientations of a blockade

Definition

Let $B = (B_{1}, \dots, B_{t})$ be a blockade and let $x \in [0, 1]$ . A sparse orientation of $B$ is an orientation of the complete graph on the index set $[t]$ such that whenever the edge $i \to j$ is oriented from $i$ to $j$ , the block $B_{i}$ is $x$ -sparse to $B_{j}$ in the sense of Sparsity of one vertex set to another, and weak sparsity of a pair.

The order orientation $i \to j$ for $i > j$ is the one built into the definition of an $x$ -sparse blockade (Complete, anticomplete, pure, weakly sparse, and $x$ -sparse blockades).

Depends on

Used by

Dependency tree · two levels

8 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

T. H. Nguyen, Notes on Recent Work on the Erdős–Hajnal Conjecture (standard reference, not scraped)
Shenwei Huang, Yiao Ju, and Yidong Zhou, Erdős-Hajnal beyond the five-vertex path (standard reference, not scraped)