On a graph packing conjecture by Bollobás, Eldridge and Catlin
✍ Scribed by Hemanshu Kaul; Alexandr Kostochka; Gexin Yu
- Publisher
- Springer-Verlag
- Year
- 2008
- Tongue
- English
- Weight
- 457 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0209-9683
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📜 SIMILAR VOLUMES
## Abstract It is shown that, for all sufficiently large __k__, the complete graph __K~n~__ can be decomposed into __k__ factors of diameter 2 if and only if __n__ ≥ 6__k__.
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) .
In this note we improve significantly the result appeared in [4] by showing that any sequence of trees { T2, 'I;, . , T,} can be packed into the complete bipartite graph K,\_,,n,z (n even) for f = 0.3n. Furthermore we support Fishburn's Conjecture [2] by showing that any sequence {T,, T4,