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- W4290802051 abstract "For a graph whose vertex set is a finite set of points in the Euclidean $d$-space consider the closed (open) balls with diameters induced by its edges. The graph is called a (an open) Tverberg graph if these closed (open) balls intersect. Using the idea of halving lines, we show that ($i$) for any finite set of points in the plane, there exists a Hamiltonian cycle that is a Tverberg graph; ($ii$) for any $ n $ red and $ n $ blue points in the plane, there exists a perfect red-blue matching that is a Tverberg graph. Also, we prove that ($iii$) for any even set of points in the Euclidean $ d $-space, there exists a perfect matching that is an open Tverberg graph; ($iv$) for any $ n $ red and $ n $ blue points in the Euclidean $ d $-space, there exists a perfect red-blue matching that is a Tverberg graph." @default.
- W4290802051 created "2022-08-12" @default.
- W4290802051 creator A5043025068 @default.
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- W4290802051 date "2021-08-22" @default.
- W4290802051 modified "2023-09-26" @default.
- W4290802051 title "Intersecting diametral balls induced by a geometric graph" @default.
- W4290802051 doi "https://doi.org/10.48550/arxiv.2108.09795" @default.
- W4290802051 hasPublicationYear "2021" @default.
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