Partitioning into graphs with only small components

Partitioning into graphs with only small components

The paper presents several results on edge partitions and vertex partitions of graphs into graphs with bounded size components. We show that every graph of bounded tree-width and bounded maximum degree admits such partitions. We also show that an arbitrary graph of maximum degree four has a vertex partition into two graphs, each of which has components on at most 57 vertices. Some generalizatio...

Partitioning into Two Graphs with Only Small Components

The paper presents several results on edge partitions and vertex partitions of graphs into graphs with bounded size components. We show that every graph of bounded tree-width and bounded maximum degree admits such partitions. We also show that an arbitrary graph of maximum degree three has a vertex partition into two graphs, each of which has components on at most two vertices, and an edge part...

Partitioning graphs into balanced components

We consider the k-balanced partitioning problem, where the goal is to partition the vertices of an input graph G into k equally sized components, while minimizing the total weight of the edges connecting different components. We allow k to be part of the input and denote the cardinality of the vertex set by n. This problem is a natural and important generalization of well-known graph partitioni...

Partitioning Random Graphs into Monochromatic Components

Erdős, Gyárfás, and Pyber (1991) conjectured that every r-colored complete graph can be partitioned into at most r − 1 monochromatic components; this is a strengthening of a conjecture of Lovász (1975) and Ryser (1970) in which the components are only required to form a cover. An important partial result of Haxell and Kohayakawa (1995) shows that a partition into r monochromatic components is p...

Partitioning Matroids With Only Small Cocircuits