Distances in orientations of graphs

@article{Chvtal1975DistancesIO,
  title={Distances in orientations of graphs},
  author={Vasek Chv{\'a}tal and Carsten Thomassen},
  journal={J. Comb. Theory, Ser. B},
  year={1975},
  volume={24},
  pages={61-75}
}
We prove that there is a function h(k) such that every undirected graph G admits an orientation H with the following property: if an edge uv belongs to a cycle of length k in G, then uv or vu belongs to a directed cycle of length at most h(k) in H. Next, we show that every undirected bridgeless graph of radius r admits an orientation of radius at most $R^2$+r, and this bound is best possible. We consider the same problem with radius replaced by diameter. Finally, we show that the problem of… CONTINUE READING

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