A tree is called bushy if it has no vertex of degree 2. Theorem: the class of countable graphs omitting a fixed finite bushy tree with at least 5 vertices has no universal element.
Graphs omitting sums of complete graphs
โ Scribed by Cherlin, Gregory; Shi, Niandong
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 119 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
For every finite m and n there is a finite set {G 1 , . . . , G l } of countable (m โข K n )-free graphs such that every countable (m โข K n )-free graph occurs as an induced subgraph of one of the graphs G i .
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