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A long-standing conjecture by Heath, Pemmaraju, and Trenk states that the upward book thickness of outerplanar DAGs is bounded above by a constant. In this paper, we show that the conjecture holds for subfamilies of upward outerplanar graphs, namely those whose underlying graph is an internally-triangulated outerpath or a cactus, and those whose biconnected components are $at$-outerplanar graphs. On the complexity side, it is known that deciding whether a graph has upward book thickness $k$ is NP-hard for any fixed $k ge 3$. We show that the problem, for any $k ge 5$, remains NP-hard for graphs whose domination number is $O(k)$, but it is FPT in the vertex cover number.
We analyze a directed variation of the book embedding problem when the page partition is prespecified and the nodes on the spine must be in topological order (upward book embedding). Given a directed acyclic graph and a partition of its edges into $k
In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Minimum Spanning Tree problem on a complete graph with $n$ nodes. The best know
We present a new $4$-approximation algorithm for the Combinatorial Motion Planning problem which runs in $mathcal{O}(n^2alpha(n^2,n))$ time, where $alpha$ is the functional inverse of the Ackermann function, and a fully distributed version for the sa
We study $k$-page upward book embeddings ($k$UBEs) of $st$-graphs, that is, book embeddings of single-source single-sink directed acyclic graphs on $k$ pages with the additional requirement that the vertices of the graph appear in a topological order
We completely determine the complexity status of the dominating set problem for hereditary graph classes defined by forbidden induced subgraphs with at most five vertices.