Packing d-degenerate graphs

被引：10
|
作者：
Bollobas, Bela [1 ,2 ]
Kostochka, Alexandr [3 ,4 ]
Nakprasit, Kittikorn [3 ]
机构：
[1] Univ Memphis, Memphis, TN 38152 USA
[2] Univ Cambridge Trinity Coll, Cambridge CB2 1TQ, England
[3] Univ Illinois, Urbana, IL 61801 USA
[4] Inst Math, Novosibirsk 630090, Russia
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 2008年 / 98卷 / 01期
基金：
美国国家科学基金会;
关键词：
graph packing; d-degenerate graphs; maximum degree;
D O I：
10.1016/j.jctb.2007.05.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study packings of graphs with given maximal degree. We shall prove that the (hitherto unproved) Bollobas-Eldridge-Catlin Conjecture holds in a considerably stronger form if one of the graphs is d-degenerate for d not too large: if d, Delta(1), Delta(2) >= 1 and n > max(40 Delta(1) 1n Delta(2), 40d Delta(2)) then a d-degenerate graph of maximal degree Delta(1) and a graph of order n and maximal degree Delta(2) pack. We use this result to show that, for d fixed and n large enough, one can pack n/1500d(2) arbitrary d-degenerate n-vertex graphs of maximal degree at most n/1000d 1n n. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：85 / 94
页数：10
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