We formalize the construction of Paterson’s variant of the Ajtai–Koml´os–Szemer´edi sorting network of logarithmic depth in the bounded arithmetical theory VNC1 ∗ (an ex...
Θk-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to...
Nicolas Bonichon, Cyril Gavoille, Nicolas Hanusse,...
We study the edge-coloring problem in the message-passing model of distributed computing. This is one of the most fundamental problems in this area. Currently, the best-known dete...
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the re...
A three-dimensional grid drawing of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line-segments representing the edges ...