Ample simplicial complexes
Ample simplicial complexes
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DOI：
10.1007/s40879-021-00521-5
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发表时间：
2020-12
影响因子：
0.6
通讯作者：
Chaim Even-Zohar;M. Farber;Lewis Mead
中科院分区：
文献类型：
--
作者：
Chaim Even-Zohar;M. Farber;Lewis Mead
Motivated by potential applications in network theory, engineering and computer science, we studyr-ample simplicial complexes. These complexes can be viewed as finite approximations to the Rado complex which has a remarkable property ofindestructibility,in the sense that removing any finite number of its simplexes leaves a complex isomorphic to itself. We prove that anr-ample simplicial complex is simply connected and 2-connected forrlarge. The numbernof vertexes of anr-ample simplicial complex satisfies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\exp \bigl (\Omega \bigl (\frac{2^r}{\sqrt{r}}\bigr )\bigr )$$\end{document}. We use the probabilistic method to establish the existence ofr-ample simplicial complexes withnvertexes for any. Finally, we introduce theiterated Paley simplicial complexes, which are explicitly constructedr-ample simplicial complexes with nearly optimal number of vertexes.
Motivated by potential applications in network theory, engineering and computer science, we studyr-ample simplicial complexes. These complexes can be viewed as finite approximations to the Rado complex which has a remarkable property ofindestructibility,in the sense that removing any finite number of its simplexes leaves a complex isomorphic to itself. We prove that anr-ample simplicial complex is simply connected and 2-connected forrlarge. The numbernof vertexes of anr-ample simplicial complex satisfies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\exp \bigl (\Omega \bigl (\frac{2^r}{\sqrt{r}}\bigr )\bigr )$$\end{document}. We use the probabilistic method to establish the existence ofr-ample simplicial complexes withnvertexes for any. Finally, we introduce theiterated Paley simplicial complexes, which are explicitly constructedr-ample simplicial complexes with nearly optimal number of vertexes.