改进的Chen-Chvátal猜想的下界

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2025-03-14 DOI:10.1007/s00493-025-00137-3

Congkai Huang

引用次数: 0

摘要

我们证明了在任何没有直线包含所有点的度规空间中，至少存在\(\Omega (n^{2/3})\)条直线。这改进了前面一般度量空间中行数的\(\Omega (\sqrt{n})\)下界，也改进了前面由连通图生成的度量空间中行数的\(\Omega (n^{4/7})\)下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Improved Lower Bound Towards Chen–Chvátal Conjecture

We prove that in every metric space where no line contains all the points, there are at least \(\Omega (n^{2/3})\) lines. This improves the previous \(\Omega (\sqrt{n})\) lower bound on the number of lines in general metric space, and also improves the previous \(\Omega (n^{4/7})\) lower bound on the number of lines in metric spaces generated by connected graphs.

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来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.