We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: • Vertex Cover is Unique Games-hard to approximate to within a factor 2−(...
We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geo...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...
We present a distributed algorithm that finds a maximal edge packing in O(∆ + log∗ W) synchronous communication rounds in a weighted graph, independent of the number of nodes...
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 ...