小独立数图形中的 H 因子

IF 1.2 1区 数学 Q1 MATHEMATICS
Ming Chen , Jie Han , Guanghui Wang , Donglei Yang
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引用次数: 0

摘要

设 H 是一个 h 顶点图。H 的顶点嵌套度 ar(H) 是最小整数 r,使得 V(H) 可以被分割成 r 部分,且每个部分都在 H 中诱导出一个森林。我们证明,对于足够大的 n∈hN,δ(G)≥max{(1-2f(H)+o(1))n,(12+o(1))n} 且 α(G)=o(n)的每个 n 顶点图 G 都包含一个 H 因子,其中 f(H)=2ar(H) 或 2ar(H)-1。这一结果可以看作是拉姆齐-图兰理论中的阿隆-尤斯特定理[1],它概括了巴洛格-莫拉-谢里夫扎德[2]和克尼林-苏[21]关于簇因子的结果。特别是,对于无限多的非小块图 H 来说,度条件是渐近尖锐的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
H-factors in graphs with small independence number

Let H be an h-vertex graph. The vertex arboricity ar(H) of H is the least integer r such that V(H) can be partitioned into r parts and each part induces a forest in H. We show that for sufficiently large nhN, every n-vertex graph G with δ(G)max{(12f(H)+o(1))n,(12+o(1))n} and α(G)=o(n) contains an H-factor, where f(H)=2ar(H) or 2ar(H)1. The result can be viewed an analogue of the Alon–Yuster theorem [1] in Ramsey–Turán theory, which generalizes the results of Balogh–Molla–Sharifzadeh [2] and Knierim–Su [21] on clique factors. In particular the degree conditions are asymptotically sharp for infinitely many graphs H which are not cliques.

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来源期刊
CiteScore
2.70
自引率
14.30%
发文量
99
审稿时长
6-12 weeks
期刊介绍: The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.
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