On preserving full orientability of graphs

Hsin-Hao Lai, Ko-Wei Lih
2010 European journal of combinatorics (Print)  
Suppose that D is an acyclic orientation of the graph G. An arc of D is dependent if its reversal creates a directed cycle. Let d min (G) (d max (G)) denote the minimum (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 k dependent arcs for every k satisfying d min (G) k d max (G). In this paper, we study conditions under which full orientability of a graph can be preserved when the graph is
more » ... ed by attaching new paths or cycles. Preservation theorems are applied to prove full orientability of subdivisions of Halin graphs and graphs of maximum degree at most three. We also characterize their d min (G).
doi:10.1016/j.ejc.2009.03.024 fatcat:c3rftnlf2fhatdpcje6e3kusdq