We provide the first non-trivial result on dynamic breadth-first search (BFS) in external-memory: For general sparse undirected graphs of initially n nodes and O(n) edges and monot...
It is well known that every bipartite graph with vertex classes of size n whose minimum degree is at least n/2 contains a perfect matching. We prove an analogue of this result for...
We give a new upper bound for the rectilinear crossing number cr(n) of the complete geometric graph Kn. We prove that cr(n) ≤ 0.380559 ¡n 4 ¢ + Θ(n3 ) by means of a new const...
—Symmetry breaking is a fundamental operation in distributed computing. It has applications to important problems such as graph vertex and edge coloring, maximal independent sets...
We show that for any > 0, a maximum-weight triangle in an undirected graph with n vertices and real weights assigned to vertices can be found in time O(n + n2+), where is the ...