On DP-Coloring of Digraphs

DP-coloring is a relatively new coloring concept by Dvo\v{r}\'ak and Postle and was introduced as an extension of list-colorings of (undirected) graphs. It transforms the problem of finding a list-coloring of a given graph $G$ with a list-assignment $L$ to finding an independent transversal in an auxiliary graph with vertex set $\{(v,c) ~|~ v \in V(G), c \in L(v)\}$. In this paper, we extend the definition of DP-colorings to digraphs using the approach from Neumann-Lara where a coloring of a digraph is a coloring of the vertices such that the digraph does not contain any monochromatic directed cycle. Furthermore, we prove a Brooks' type theorem regarding the DP-chromatic number, which extends various results on the (list-)chromatic number of digraphs.Comment: 23 pages, 6 figure

Development of Nanocomposite Powders for the SLS Process to Enhance Mechanical Properties

In an effort to fabricate prototypes with improved mechanical properties in the dual laser sintering process, functionalized graphite nanoplatelets were added to the PA-12 powder to produce a nanocomposite powder. The PA-12 powder was chosen as the matrix polymer because it has features conducive to laser sintering such as relatively low melting temperature and high mechanical properties. The GNPs were oxidized through a nitric acid treatment to improve the interfacial bonding. The resulting nanocomposite powder was layered and sintered by laser without any sign of agglomeration. Although the result is preliminary, it nevertheless shows the suitability of the nanocomposite powder for the laser sintering process.Mechanical Engineerin