The Densest k-subgraph problem (i.e. find a size k subgraph with maximum number of edges), is one of the notorious problems in approximation algorithms. There is a significant g...
In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dom...
In the minimum path coloring problem, we are given a graph and a set of pairs of vertices of the graph and we are asked to connect the pairs by colored paths in such a way that pa...
A coloring is proper if each color class induces connected components of order one (where the order of a graph is its number of vertices). Here we study relaxations of proper two-c...
The Jordan Curve Theorem (JCT) states that a simple closed curve divides the plane into exactly two connected regions. We formalize and prove the theorem in the context of grid gr...