Partitioning into graphs with only small components

Noga Alon; Guoli Ding; Bogdan Oporowski; Dirk Vertigan

doi:10.1016/S0095-8956(02)00006-0

Partitioning into graphs with only small components

Noga Alon, Guoli Ding, Bogdan Oporowski^*, Dirk Vertigan

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

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 generalizations of the last result are also discussed.

Original language	English
Pages (from-to)	231-243
Number of pages	13
Journal	Journal of Combinatorial Theory. Series B
Volume	87
Issue number	2
DOIs	https://doi.org/10.1016/S0095-8956(02)00006-0
State	Published - Mar 2003

Keywords

Edge partitions
Small components
Tree-width
Vertex partitions

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10.1016/S0095-8956(02)00006-0

Cite this

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title = "Partitioning into graphs with only small components",

abstract = "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 generalizations of the last result are also discussed.",

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author = "Noga Alon and Guoli Ding and Bogdan Oporowski and Dirk Vertigan",

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T1 - Partitioning into graphs with only small components

AU - Alon, Noga

AU - Ding, Guoli

AU - Oporowski, Bogdan

AU - Vertigan, Dirk

PY - 2003/3

Y1 - 2003/3

N2 - 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 generalizations of the last result are also discussed.

AB - 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 generalizations of the last result are also discussed.

KW - Edge partitions

KW - Small components

KW - Tree-width

KW - Vertex partitions

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EP - 243

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

IS - 2

ER -

Partitioning into graphs with only small components

Abstract

Keywords

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