A note on the colorful fractional Helly theorem

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• 作者：Minki Kim ^{kmk90@kaist.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Helly&rsquo ; s theorem ; Colorful Helly theorem ; Fractional Helly theorem
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：6 January 2017
• 年：2017
• 卷：340
• 期：1
• 页码：3167-3170
• 全文大小：371 K

文摘

Helly’s theorem is a classical result concerning the intersection patterns of convex sets in R^d${\mathbb{R}}^d$. Two important generalizations are the colorful version and the fractional version. Recently, Bárány et al. combined the two, obtaining a colorful fractional Helly theorem. In this paper, we give an improved version of their result.