In this paper, we present a polynomial dynamic programming algorithm that tests whether a n-vertex directed tree T has an upward planar embedding into a convex point-set S of size n. Further, we extend our approach to the class of outerplanar digraphs. This nontrivial and surprising result implies that any given digraph can be efficiently tested for an upward planar embedding into a given conve...

With each superinuitionistic logic (si-logic), we associate its downward and upward subframizations, and characterize them by means of Zakharsyachev’s canonical formulas, as well as by embedding si-logics into the extensions of the propositional lax logic PLL. In an analogous fashion, with each si-logic, we associate its downward and upward stabilizations, and characterize them by means of stab...

We study monotone simultaneous embeddings of upward planar digraphs, which are simultaneous embeddings where the drawing of each digraph is upward planar, and the directions of the upwardness of different graphs can differ. We first consider the special case where each digraph is a directed path. In contrast to the known result that any two directed paths admit a monotone simultaneous embedding...

In this paper we study the problem of existence of a crossing-free acyclic hamiltonian path completion (for short, HP-completion) set for embedded upward planar digraphs. In the context of book embeddings, this question becomes: given an embedded upward planar digraph G, determine whether there exists an upward 2-page book embedding of G preserving the given planar embedding. Given an embedded ...

An upward planar drawing of a digraph G is a planar drawing of G where every edge is drawn as a simple curve monotone in the vertical direction. A digraph is upward planar if it has an embedding that admits an upward planar drawing. The problem of testing whether a digraph is upward planar is NP-complete. In this paper we give a linear-time algorithm to test the upward planarity of a series-par...

Giordano, Liotta and Whitesides [1] developed an algorithm that, given an embedded planar st-digraph and a topological numbering ρ of its vertices, computes in O(n) time a ρ-constrained upward topological book embedding with at most 2n−4 spine crossings per edge. The number of spine crossings per edge is asymptotically worst case optimal. In this poster, we present improved results with respect...

In this paper we study the problem of computing an upward straight-line embedding of a directed graph G into a point set S, i.e. a planar drawing of G such that each vertex is mapped to a point of S, each edge is drawn as a straight-line segment, and all the edges are oriented according to a common direction. We characterize the family of directed graphs that admit an upward straight-line embed...

In this paper we study the problem of computing an upward straight-line embedding of a directed graph G into a point set S, i.e. a planar drawing of G such that each vertex is mapped to a point of S, each edge is drawn as a straight-line segment, and all the edges are oriented according to a common direction. We characterize the family of directed graphs that admit an upward straight-line embed...

We give a complete and elementary proof of the following upward categoricity theorem: LetK be a local abstract elementary class with amalgamation and joint embedding, arbitrarily large models, and countable LöwenheimSkolem number. If K is categorical in א1 then K is categorical in every uncountable cardinal. In particular, this provides a new proof of the upward part of Morley’s theorem in firs...