On the chromatic index of almost all graphs
✍ Scribed by P Erdős; Robin J Wilson
- Book ID
- 107884067
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 149 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
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## Abstract A homomorphism from an oriented graph __G__ to an oriented graph __H__ is a mapping $\varphi$ from the set of vertices of __G__ to the set of vertices of __H__ such that $\buildrel {\longrightarrow}\over {\varphi (u) \varphi (v)}$ is an arc in __H__ whenever $\buildrel {\longrightarrow}
## Abstract Erdös proved that there exist graphs of arbitrarily high girth and arbitrarily high chromatic number. We give a different proof (but also using the probabilistic method) that also yields the following result on the typical asymptotic structure of graphs of high girth: for all ℓ ≥ 3 and