Alphabeta MathHow statement and proof provenance work
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The -overlap blockade and its iterated mixed quotients
Definition
For a comb block , suppose and let be the ordered blockade whose blocks are the -overlap classes in , ordered by their least vertex in a fixed ordering of . Having defined , put where is its mixed-block reachability relation. These are the iterated mixed quotients of the -overlap blockade.
Depends on
Used by
- An H₅-overlap class and its terminal quotient Example
- In a special-vertex comb of a co-E-free graph, vertices in other comb blocks remain pure to every H₅-overlap quotient block Lemma
- Iterated mixed quotients of an H₅-overlap blockade terminate at a pure blockade Lemma
- The pattern of the terminal H₅-overlap quotient is {H₅,co-E}-free Lemma
- A special-vertex comb in a co-E-free graph admits the {H₅,co-E} structural partition Theorem
Dependency tree · two levels
6 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
- Huang, Ju, and Zhou, Erdős-Hajnal beyond the five-vertex path, proof of Lemma 6.4 (standard reference, not scraped)