完美混合倾斜的充分条件

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2024-09-24 DOI:10.1016/j.jctb.2024.08.007

Eoin Hurley , Felix Joos , Richard Lang

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引用次数: 0

摘要

我们开发了一种方法来研究完美混合倾斜的充分条件。我们的框架允许嵌入具有亚线性阶成分的有界阶图 H。作为推论，我们恢复并扩展了库恩（Kühn）和奥斯特胡斯（Osthus）的工作，即用上述图 H 替换 F-tiling，从而获得完美 F-tiling（对于任意固定图 F）的最小阶数充分条件。最后，我们在强意义上渐近地解决了孔洛斯的一个猜想。

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Sufficient conditions for perfect mixed tilings

We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs H with components of sublinear order. As a corollary, we recover and extend the work of Kühn and Osthus regarding sufficient minimum degree conditions for perfect F-tilings (for an arbitrary fixed graph F) by replacing the F-tiling with the aforementioned graphs H. Moreover, we obtain analogous results for degree sequences and in the setting of uniformly dense graphs. Finally, we asymptotically resolve a conjecture of Komlós in a strong sense.

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

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.