Sharing tea on a graph ...
arXiv, 2024
academicJournal
Zugriff:
Motivated by the analysis of consensus formation in the Deffuant model for social interaction, we consider the following procedure on a graph $G$. Initially, there is one unit of tea at a fixed vertex $r \in V(G)$, and all other vertices have no tea. At any time in the procedure, we can choose a connected subset of vertices $T$ and equalize the amount of tea among vertices in $T$. We prove that if $x \in V(G)$ is at distance $d$ from $r$, then $x$ will have at most $\frac{1}{d+1}$ units of tea during any step of the procedure. This bound is best possible and answers a question of Gantert. We also consider arbitrary initial weight distributions. For every finite graph $G$ and $w \in \mathbb{R}_{\geq 0}^{V(G)}$, we prove that the set of weight distributions reachable from $w$ is a compact subset of $\mathbb{R}_{\geq 0}^{V(G)}$. ... : 19 pages, 2 figures ...
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Sharing tea on a graph ...
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Autor/in / Beteiligte Person: | Gollin, J. Pascal ; Hendrey, Kevin ; Huang, Hao ; Huynh, Tony ; Mohar, Bojan ; Oum, Sang-il ; Yang, Ningyuan ; Yu, Wei-Hsuan ; Zhu, Xuding |
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Veröffentlichung: | arXiv, 2024 |
Medientyp: | academicJournal |
DOI: | 10.48550/arxiv.2405.15353 |
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