A note on the colorful fractional Helly theorem

详细信息    查看全文

• 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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16302229&_mathId=si1.gif&_user=111111111&_pii=S0012365X16302229&_rdoc=1&_issn=0012365X&md5=26cdec0396d6fd37f860f2a5fd1087f9" title="Click to view the MathML source">R^dclass="mathContainer hidden">class="mathCode">${\mathbb{R}}^d$. 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.