A note on orientations of mixed graphs
Discrete Applied Mathematics
On the orientation of graphs and hypergraphs
Discrete Applied Mathematics - Submodularity
AT-free graphs: linear bounds for the oriented diameter
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
On the diameter of Eulerian orientations of graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Complexity of approximating the oriented diameter of chordal graphs
Journal of Graph Theory
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
The edge-orientation problem and some of its variants on weighted graphs
Information Sciences: an International Journal
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Let G be an undirected 2-edge connected graph with nonnegative edge weights and a distinguished vertex z. For every node consider the shortest cycle containing this node and z in G. The cycle-radius of G is the maximum length of a cycle in this set. Let H be a directed graph obtained by directing the edges of G. The cycle-radius of H is similarly defined except that cycles are replaced by directed closed walks. We prove that there exists for every nonnegative edge weight function an orientation H of G whose cycle-radius equals that of G if and only if G is series-parallel.