We consider the problem of constructing bounded-degree planar geometric spanners of Euclidean and unit-disk graphs. It is well known that the Delaunay subgraph is a planar geometri...
We investigate the following vertex percolation process. Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p = n-...
Catherine S. Greenhill, Fred B. Holt, Nicholas C. ...
This paper proposes a method for reducing the maximum degree of vertices in graphs that maintain optimal broadcast time when a vertex can call a vertex at distance at most k durin...
The rigidity of squares of graphs in three-space has important applications to the study of flexibility in molecules. The Molecular Conjecture, posed in 1984 by T-S. Tay and W. Wh...
The main result of this paper is that every 4-uniform hypergraph on n vertices and m edges has a transversal with no more than (5n + 4m)/21 vertices. In the particular case n = m,...