## Abstract The Erdős‐Sós Conjecture is that a finite graph __G__ with average degree greater than __k__ − 2 contains every tree with __k__ vertices. Theorem 1 is a special case: every __k__‐vertex tree of diameter four can be embedded in __G__. A more technical result, Theorem 2, is obtained by ex
The Erdős–Sós Conjecture for Graphs withoutC4
✍ Scribed by Jean-François Saclé; Mariusz Woźniak
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 279 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
For any integer r \ 1, let a(r) be the largest constant a \ 0 such that if E > 0 and 0 < c < c 0 for some small c 0 =c 0 (r, E) then every graph G of sufficiently large order n and at least edges contains a copy of any (r+1)-chromatic graph H of independence number a(H) [ (a -E) log n log(1/c) .
Let H and G be graph classes. We say that H has the Erd" os-Pósa property for G if for any graph G ∈ G, the minimum vertex covering of all H-subgraphs of G is bounded by a function f of the maximum packing of H-subgraphs in G (by H-subgraph of G we mean any subgraph of G that belongs to H). Robertso
## Abstract The Erdős‐Rényi and Projective Norm graphs are algebraically defined graphs that have proved useful in supplying constructions in extremal graph theory and Ramsey theory. Their eigenvalues have been computed and this yields an upper bound on their independence number. Here we show that