A common variable minimax theorem for graphs
Abstract
Let $\mathcal{G} = \{G_1 = (V, E_1), \dots, G_m = (V, E_m)\}$ be a collection of $m$ graphs defined on a common set of vertices $V$ but with different edge sets $E_1, \dots, E_m$. Informally, a function $f :V \rightarrow \mathbb{R}$ is smooth with respect to $G_k = (V,E_k)$ if $f(u) \sim f(v)$ whenever $(u, v) \in E_k$. We study the problem of understanding whether there exists a nonconstant function that is smooth with respect to all graphs in $\mathcal{G}$, simultaneously, and how to find it if it exists.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2107.14747
- arXiv:
- arXiv:2107.14747
- Bibcode:
- 2021arXiv210714747C
- Keywords:
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- Mathematics - Spectral Theory;
- Computer Science - Machine Learning
- E-Print:
- 21 pages, 11 figures