Alphabeta MathComb Structure in co-Bird-Free Graphs — Examples
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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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1 · Prerequisites
- Blockades, Combs and Pattern Graphs
- Comb Structure in co-Bird-Free Graphs
- Construction of the Natural Numbers
- Construction of the Real Numbers via Cauchy Sequences
- Construction of the Real Numbers via Dedekind Cuts
- Countability and Uncountability
- Finite Counting, Factorials and Binomial Coefficients
- Foundations of the Real Numbers for Analysis
- Graphs, Walks and Connectivity
- Induced Subgraphs and Hereditary Graph Classes
- Leaf Reducibility and Wonderful Families
- Quotient Blockades and Mixing Relations
- Regular Pairs and Induced Counting
- Relations, Functions, and Quotients
- Roots, Rational Powers, and Classical Inequalities
- Small-Graph Erdős-Hajnal Consequences
- Sparse Restricted Subgraphs and the Rödl–Nikiforov Theorems
- The ZFC Axioms and the Basic Set Constructions
2 · Logical flowchart
3 · Items
Example
The first co-Bird witness by adjacency
Example
The second co-Bird witness by adjacency
Example
All E neighbourhood patterns under a complete nonedge pair
Example
The no-E-copy boundary case of the comb partition
Sources
- Huang–Ju–Zhou, Erdős–Hajnal beyond the five-vertex path, §6.2, Figure 9, first witness
- Huang–Ju–Zhou, Erdős–Hajnal beyond the five-vertex path, §6.2, Figure 9, second witness
- Huang–Ju–Zhou, Erdős–Hajnal beyond the five-vertex path, §6.2, Claim 6.5.2, explicit finite expansion
- Huang–Ju–Zhou, Erdős–Hajnal beyond the five-vertex path, §6.2, Lemma 6.5, singleton boundary adaptation