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

75 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
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 - 1 Mar 2003
Externally published	Yes

Keywords

Edge partitions
Small components
Tree-width
Vertex partitions

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

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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AU - Alon, Noga

AU - Ding, Guoli

AU - Oporowski, Bogdan

AU - Vertigan, Dirk

PY - 2003/3/1

Y1 - 2003/3/1

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

UR - https://www.scopus.com/pages/publications/0037374155

U2 - 10.1016/S0095-8956(02)00006-0

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

M3 - Article

AN - SCOPUS:0037374155

SN - 0095-8956

VL - 87

SP - 231

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

ASJC Scopus subject areas

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