Arc-Disjoint Paths and Trees in 2-Regular Digraphs

An out-(in-)branching B_s^+ (B_s^-) rooted at s in a digraph D is a connected spanning subdigraph of D in which every vertex x != s has precisely one arc entering (leaving) it and s has no arcs entering (leaving) it. We settle the complexity of the following two problems: 1) Given a 2-regular digraph $D$, decide if it contains two arc-disjoint branchings B^+_u, B^-_v. 2) Given a 2-regular digraph D, decide if it contains an out-branching B^+_u such that D remains connected after removing the arcs of B^+_u. Both problems are NP-complete for general digraphs. We prove that the first problem remains NP-complete for 2-regular digraphs, whereas the second problem turns out to be polynomial when we do not prescribe the root in advance. We also prove that, for 2-regular digraphs, the latter problem is in fact equivalent to deciding if $D$ contains two arc-disjoint out-branchings. We generalize this result to k-regular digraphs where we want to find a number of pairwise arc-disjoint spanning trees and out-branchings such that there are k in total, again without prescribing any roots.Comment: 9 pages, 7 figure

Finding an induced subdivision of a digraph

We consider the following problem for oriented graphs and digraphs: Given an oriented graph (digraph) $G$, does it contain an induced subdivision of a prescribed digraph $D$? The complexity of this problem depends on $D$ and on whether $G$ must be an oriented graph or is allowed to contain 2-cycles. We give a number of examples of polynomial instances as well as several NP-completeness proofs

Outsourcing of activities related to international transportation of system packages for ships in Havyard

Confidential until 3 January 201

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

Den digitaliserede Kulturarv - En læringsressource med stort potentiale!

Artiklen diskuterer læringspotentialet i den digitaliserede kulturarv dels i et kulturelt perspektiv (kulturarv som national, europæisk og global indikator med potentiale for øget identitetsdannelse og mellemfolkelig forståelse), dels i et læringsteoretisk perspektiv (store åbne læringsressourcer som udgangspunkt for læringsaktiviteter med fokus på sam‐arbejde i problembaseret projektarbejde). Udgangspunktet tages i den nye europæske database for den digitaliserede kulturarv Europeana og erfaringer fra et dansk digitaliseringsprojekt vedrørende digitalisering af biografreklamefilm og TV2 reklamer.Samtidig fokuserer artiklen på behovet for at udvikle/integrere nye samarbejdsvæktøjer i læreprocessen (Web 2.0, annoterings-, segmenterings- og genkendelsesvæktøer, mm.) med henblik på samarbejde som en integreret del af læingsaktiviteterne.Sidst i artiklen diskuteres det om en øget adgang til digitale læringsressourcer, der kan udbygges med brugergenereret indhold og øget tilgængelighed via fremtidens mobile teknologier, rummer et potentiale for en ny oplysningstid