Chordal Graphs are Fully Orientable

Details Chordal Graphs are Fully Orientable Chordal Graphs are Fully Orientable

2012-02-26

arxiv.org/abs/1202.5718v1

Mathematics

Combinatorics

11 pages, 1 figure, accepted by Ars Combinatoria (March 26, 2010)

Scientific paper

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 orientable.

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