Let D ∈ D(n, p) denote a simple random digraph obtained by choosing each of the ` n 2 ́ undirected edges independently with probability 2p and then orienting each chosen edge independently in one of the two directions with equal probability 1/2. Let mas(D) denote the maximum size of an induced acyclic subgraph in D. We obtain tight concentration results on the size of mas(D). Precisely, we show ...

We study the equivalence relation on the set of acyclic orientations of an undirected graph Γ generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in tur...

Graph drawing and visualization represent structural information as diagrams of abstract graphs and networks. E-Spring Algorithm, derived from the popular spring embedder model, was proposed to eliminate node overlaps in the drawings of clustered directed acyclic graphs Gc. In this paper, we apply the E-Spring algorithm to general graphs by minimizing edge-node intersections. Initially, a tree ...

Formal rules governing signed edges on causal directed acyclic graphs are described in this paper and it is shown how these rules can be useful in reasoning about causality. Specifically, the notions of a monotonic effect, a weak monotonic effect and a signed edge are introduced. Results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an inter...

Competition graphs have appeared in a variety of applications from food webs to communication networks to energy models. The competition graph, C (D), of a digraph D has the same vertex set as D and (x; y) is an edge in C (D) if and only if there is a vertex z such that (x; z) and (y; z) are arcs in D. It has been observed that most actual food webs have interval competition graphs. Subsequent ...

Given an edge-weighted undirected graph and two vertices s and t, the next-to-shortest path problem is to find an st-path whose length is minimum among all st-paths of lengths strictly larger than the shortest path length. The problem is shown to be polynomially solvable if all edge weights are positive, while the complexity status for the nonnegative weight case was open. In this paper we show...

Every connected simple graph G has an acyclic orientation. Deene a graph AO(G) whose vertices are the acyclic orientations of G and whose edges join orientations that diier by reversing the direction of a single edge. It was known previously that AO(G) is connected but not necessarily Hamiltonian. However, Squire 3] proved that the square AO(G) 2 is Hamiltonian. We prove the slightly stronger r...

Every connected simple graph G has an acyclic orientation. Define a graph AO(G) whose vertices are the acyclic orientations of G and whose edges join orientations that differ by reversing the direction of a single edge. It was known previously that AO(G) is connected but not necessarily Hamiltonian. However, Squire [3] proved that the square AO(G) is Hamiltonian. We prove the slightly stronger ...

In this note I describe how to capture the kinematics of quantum causal evolution using a logic called BV developed by the Calculus of Structures group at Dresden. The setting is discrete quantum mechanics. We imagine a finite “web” of spacetime points. The points are events in spacetime. They are viewed as verhtees in a directed acyclic graph (DAG); the edges of the DAG represent causal links ...

graph graph and geography the geographical problem Figure 3.11: The Koenigsberg bridge problem and its graphical representation. The problem and its associated graph is shown in Figure 3.11 and this allows us to prove it is impossible to visit all the land masses, crossing each bridge only once. Graphs are a topological construct, and do not have a notion of distance associated with them in gen...