Graph Partitions:Recent Progresses and Some Open Problems

Abstract

Graph partition problem is one of the most important topics in structural graph theory, since many problems in graph theory can be treated as a partition of the vertices into sets with some properties. For instance, the classical vertex coloring problem asks for a partition into minimum number of independent sets, and the maximum k-partite subgraph problem asks for a k-partite subgraph with maximum number of edges. In this paper, we present some results and problems on graph partitions, of which most are from the topic originated from the maximum k-partite subgraph problem.