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

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

65 Scopus citations

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 (US)
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
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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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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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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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DO - 10.1016/S0095-8956(02)00006-0

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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

All Science Journal Classification (ASJC) codes

Keywords

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