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

Widening of Protostellar Outflows: an Infrared Outflow Survey in Low Luminosity Objects

We present an outflow survey toward 20 Low Luminosity Objects (LLOs), namely protostars with an internal luminosity lower than 0.2 Lsun. Although a number of studies have reported the properties of individual LLOs, the reasons for their low luminosity remain uncertain. To answer this question, we need to know the evolutionary status of LLOs. Protostellar outflows are found to widen as their parent cores evolve, and therefore, the outflow opening angle could be used as an evolutionary indicator. The infrared scattered light escapes out through the outflow cavity and highlights the cavity wall, giving us the opportunity to measure the outflow opening angle. Using the Canada-France-Hawaii Telescope, we detected outflows toward eight LLOs out of 20 at Ks band, and based on archival Spitzer IRAC1 images, we added four outflow-driving sources from the remaining 12 sources. By fitting these images with radiative transfer models, we derive the outflow opening angles and inclination angles. To study the widening of outflow cavities, we compare our sample with the young stellar objects from Arce & Sargent 2006 and Velusamy et al. 2014 in the plot of opening angle versus bolometric temperature taken as an evolutionary indicator.Our LLO targets match well the trend of increasing opening angle with bolometric temperature reported by Arce & Sargent and are broadly consistent with that reported by Velusamy et al., suggesting that the opening angle could be a good evolutionary indicator for LLOs. Accordingly, we conclude that at least 40% of the outflow-driving LLOs in our sample are young Class 0 objects.Comment: Accepted for publication in AJ, 13 pages, 9 figure