Chordal Graphs are Fully Orientable

@article{Lai2012ChordalGA,
  title={Chordal Graphs are Fully Orientable},
  author={Hsin-Hao Lai and Ko-Wei Lih},
  journal={ArXiv},
  year={2012},
  volume={abs/1202.5718}
}
Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let m and M denote the minimum and the maximum of the number of dependent arcs over all acyclic orientations of G. We call G fully orientable if G has an acyclic orientation with exactly d dependent arcs for every d satisfying m <= d <= M. A graph G is called chordal if every cycle in G of length at least four has a chord. We show that all chordal graphs are fully… CONTINUE READING

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