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Decomposing large graphs with small graphs of high density
Author(s) -
Yuster Raphael
Publication year - 1999
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199909)32:1<27::aid-jgt3>3.0.co;2-c
Subject(s) - combinatorics , mathematics , graph , integer (computer science) , discrete mathematics , computer science , programming language
It is shown that for every positive integer h , and for every ϵ > 0, there are graphs H = ) V H E H ) with at least h vertices and with density at least 0.5 ‐ ϵ with the following property: If G = ( V G , E G ) is any graph with minimum degree at least ${|V_{G}|}\over{2}$ (1 + o (1)) and | E H | divides | E G |, then G has an H ‐decomposition. This result extends the results of [R. M. Wilson, Cong Numer XV (1925), 647–659] [T. Gustavsson, Ph.D. Thesis, U. Stockholm, 1991] [R. Yuster, Random Struc Algorith, 12 (1998), 237–251]. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 27–40, 1999