Hefner, K.A.S., K.F. Jones, S. Kim, J.R. Lundgren and F.S. Roberts, (i,j) competition graphs, Discrete Applied Mathematics 32 (1991) 241-262. If D is an acyclic digraph, its competition graph has the same vertex set as D and an edge between vertices x and y if and only if for some vertex u, there are arcs (_q u) and (_Y, u) in D. We study competition graphs of acyclic digraphs D when the indegr...

This thesis studies aspects of the set of acyclic orientations of a simple undirected graph. Acyclic orientations of a graph may be readily obtained from bijective labellings of its vertex-set with a totally ordered set, and they can be regarded as partially ordered sets. We will study this connection between acyclic orientations of a graph and the theory of linear extensions or topological sor...

We contribute to the study of inferring commercial relationships between autonomous systems (AS relationships) from observable BGP routes. We deduce several forbidden patterns of AS relationships that impose a certain type of acyclicity on the AS graph. We investigate algorithms for solving the acyclic all-paths type-of-relationship problem, i.e., given a set of AS paths, find an orientation of...

The acyclic edge colouring problem is extensively studied in graph theory. The corner-stone of this field is a conjecture of Alon et. al.[1] that a′(G) ≤ ∆(G) + 2. In that and subsequent work, a′(G) is typically bounded in terms of ∆(G). Motivated by this we introduce a term gap(G) defined as gap(G) = a′(G) − ∆(G). Alon’s conjecture can be rephrased as gap(G) ≤ 2 for all graphs G. In [5] it was...

An upward topological book embedding of a planar st-digraph G is an upward planar drawing of G such that its vertices are aligned along the vertical line, called the spine, and each edge is represented as a simple Jordan curve which is divided by the intersections with the spine (spine crossings) into segments such that any two consecutive segments are located at opposite sides of the spine. Wh...

A (1, λ)-embedded graph is a graph that can be embedded on a surface with Euler characteristic λ so that each edge is crossed by at most one other edge. A graph G is called α-linear if there exists an integral constant β such that e(G′) ≤ αv(G′) + β for each G′ ⊆ G. In this paper, it is shown that every (1, λ)-embedded graph G is 4-linear for all possible λ, and is acyclicly edge-(3∆(G) + 70)-c...

Given a graph and pairs siti of terminals, the edge-disjoint paths problem is to determine whether there exist siti paths that do not share any edges. We consider this problem on acyclic digraphs. It is known to be NP-complete and solvable in time n where k is the number of paths. It has been a long-standing open question whether it is fixed-parameter tractable in k. We resolve this question in...

We present Kathaa, an Open Source web-based Visual Programming Framework for Natural Language Processing (NLP) Systems. Kathaa supports the design, execution and analysis of complex NLP systems by visually connecting NLP components from an easily extensible Module Library. It models NLP systems an edge-labeled Directed Acyclic MultiGraph, and lets the user use publicly co-created modules in the...

In information technology, big data is a term used to describe data sets so large and complex that they become awkward to work and analyze. Difficulties include capture, storage, search, sharing, analysis, and visualization. In this work we focus in the latter part, specifically we study the visualization of graphs. The need for simple and intuitive visualization techniques is more imminent tha...

Consider a network N = (V; Ec; c) with an integer valued capacity function c: V V ! Z+, and let k be a positive integer. What is the minimal total increase by which the individual capacities must be increased such that the edge connectivity number is at least k? Clearly the defect r(u) := max(k ? c(u); 0) summing over all vertices, called T is a lower bound for. Kajitani and Ueno 7] proved that...