5 research outputs found
Full Orientability of the Square of a Cycle
Let D be an acyclic orientation of a simple graph G. An arc of D is called
dependent if its reversal creates a directed cycle. Let d(D) denote the number
of dependent arcs in D. Define m and M to be the minimum and the maximum number
of d(D) over all acyclic orientations D of G. We call G fully orientable if G
has an acyclic orientation with exactly k dependent arcs for every k satisfying
m <= k <= M. In this paper, we prove that the square of a cycle C_n of length n
is fully orientable except n=6.Comment: 7 pages, accepted by Ars Combinatoria on May 26, 201
Chordal Graphs are Fully Orientable
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.Comment: 11 pages, 1 figure, accepted by Ars Combinatoria (March 26, 2010
On preserving full orientability of graphs
[[sponsorship]]數學研究所[[note]]已出版;[SCI];有審查制度;不具代表性[[note]]http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Drexel&SrcApp=hagerty_opac&KeyRecord=0195-6698&DestApp=JCR&RQ=IF_CAT_BOXPLO