We show the first o(n2 ) algorithm for coloring vertices of trianglefree planar graphs using three colors. The time complexity of the algorithm is O(n log n). Our approach can be ...
This article addresses the problem of efficient multi-robot patrolling in a known environment. The proposed approach assigns regions to each mobile agent. Every region is represen...
We consider two generalizations of the edge coloring problem in bipartite graphs. The first problem we consider is the weighted bipartite edge coloring problem where we are given a...
We consider the problem of orienting the edges of a graph so that the length of a longest path in the resulting digraph is minimum. As shown by Gallai, Roy and Vitaver, this edge ...
The Balanced Subgraph problem (edge deletion variant) asks for a 2-coloring of a graph that minimizes the inconsistencies with given edge labels. It has applications in social netw...