Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones....
For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour cl...
Louigi Addario-Berry, Louis Esperet, Ross J. Kang,...
Given a graph G, we say S V (G) is resolving if for each pair of distinct u, v V (G) there is a vertex x in S where d(u, x) = d(v, x). The metric dimension of G is the minimum c...
The vertex arboricity va(G) of a graph G is the minimum number of subsets into which the vertex set V (G) can be partitioned so that each subset induces an acyclic subgraph. The f...
We consider the problem of finding obnoxious centers in graphs. For arbitrary graphs with n vertices and m edges, we give a randomized algorithm with O(n log2 n + m log n) expecte...