Proof of a Conjecture of Bollobás and Eldridge for Graphs of Maximum Degree Three*
✍ Scribed by Béla Csaba†‡; Ali Shokoufandeh‡; Endre Szemerédi
- Publisher
- Springer-Verlag
- Year
- 2003
- Tongue
- English
- Weight
- 432 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0209-9683
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) .
## 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__.
mixed multigraph does not exceed either its edge chromatic number or its maximum degree plus one. In this note, this conjecture is proved for multigraphs with maximum degree at most 3.