Pinchasi and Radoiˇci´c [11] used the following observation to bound the number of edges of a topological graph without a self-crossing cycle of length 4: if we make a list of t...
We shall prove that for all 3 and > 0 there exists a sparse oriented graph of arbitrarily large order with oriented girth and such that any 1/2 + proportion of its arcs induc...
This paper examines directed graphs related to convex polytopes. For each fixed d-polytope and any acyclic orientation of its graph, we prove there exist both convex and concave fu...
We consider a network represented by a simple connected undirected graph with N anonymous nodes that have local orientations, i.e. incident edges of each vertex have locally-unique...
A h-uniform hypergraph H = (V, E) is called ( , k)-orientable if there exists an assignment of each hyperedge e ∈ E to exactly of its vertices v ∈ e such that no vertex is ass...