Tree Decomposition of Graphs

Raphael Yuster

doi:10.1002/(SICI)1098-2418(199805)12:3<237::AID-RSA2>3.0.CO;2-W

Tree Decomposition of Graphs

Raphael Yuster

Department of Mathematics

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

Abstract

Let H be a tree on h ≥ 2 vertices. It is shown that if G = (V, E) is a graph with δ(G) ≥ (|V|/2) + 10h⁴√|V|log|V|, and h - 1 divides |E|, then there is a decomposition of the edges of G into copies of H. This result is asymptotically the best possible for all trees with at least three vertices.

Original language	English
Pages (from-to)	237-251
Number of pages	15
Journal	Random Structures and Algorithms
Volume	12
Issue number	3
DOIs	https://doi.org/10.1002/(SICI)1098-2418(199805)12:3<237::AID-RSA2>3.0.CO;2-W
State	Published - May 1998

Keywords

Decomposition
Trees

ASJC Scopus subject areas

Software
General Mathematics
Computer Graphics and Computer-Aided Design
Applied Mathematics

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10.1002/(SICI)1098-2418(199805)12:3<237::AID-RSA2>3.0.CO;2-W

Cite this

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title = "Tree Decomposition of Graphs",

abstract = "Let H be a tree on h ≥ 2 vertices. It is shown that if G = (V, E) is a graph with δ(G) ≥ (|V|/2) + 10h4√|V|log|V|, and h - 1 divides |E|, then there is a decomposition of the edges of G into copies of H. This result is asymptotically the best possible for all trees with at least three vertices.",

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author = "Raphael Yuster",

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AU - Yuster, Raphael

PY - 1998/5

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N2 - Let H be a tree on h ≥ 2 vertices. It is shown that if G = (V, E) is a graph with δ(G) ≥ (|V|/2) + 10h4√|V|log|V|, and h - 1 divides |E|, then there is a decomposition of the edges of G into copies of H. This result is asymptotically the best possible for all trees with at least three vertices.

AB - Let H be a tree on h ≥ 2 vertices. It is shown that if G = (V, E) is a graph with δ(G) ≥ (|V|/2) + 10h4√|V|log|V|, and h - 1 divides |E|, then there is a decomposition of the edges of G into copies of H. This result is asymptotically the best possible for all trees with at least three vertices.

KW - Decomposition

KW - Trees

UR - https://www.scopus.com/pages/publications/0032387781

U2 - 10.1002/(SICI)1098-2418(199805)12:3<237::AID-RSA2>3.0.CO;2-W

DO - 10.1002/(SICI)1098-2418(199805)12:3<237::AID-RSA2>3.0.CO;2-W

M3 - Article

AN - SCOPUS:0032387781

SN - 1042-9832

VL - 12

SP - 237

EP - 251

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 3

ER -

Tree Decomposition of Graphs

Abstract

Keywords

ASJC Scopus subject areas

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