For a graph G, denote by fk(G) the smallest number of vertices that must be deleted from G so that the remaining induced subgraph has its maximum degree shared by at least k verti...
We present a technique for transforming classical approximation algorithms into constant-time algorithms that approximate the size of the optimal solution. Our technique is applic...
We show that the firefighter problem is NP-complete for cubic graphs. We also show that given a rooted tree of maximum degree three in which every leaf is the same distance from t...
We prove that for all 0 ≤ t ≤ k and d ≥ 2k, every graph G with treewidth at most k has a ‘large’ induced subgraph H, where H has treewidth at most t and every vertex in ...
A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. The domatic number problem is that of partitioning the vertices of a gra...