We consider the problem of testing 3-colorability in the bounded-degree model. We show that, for small enough ε, every tester for 3colorability must have query complexity Ω(n)....
We study approximation algorithms, integrality gaps, and hardness of approximation, of two problems related to cycles of "small" length k in a given graph. The instance f...
We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP...
Michal Malafiejski, Krzysztof Giaro, Robert Jancze...
We consider the problem of finding a minimum diameter spanning tree with maximum node degree B in a complete undirected edge-weighted graph. We provide an O( p logB n)-approximatio...
The connectivity index w(G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where is a real number ( = 0), and d(u) denotes the degree of the vertex u. Le...