A Common Variable Minimax Theorem for Graphs

Let [Formula omitted] be a collection of m graphs defined on a common set of vertices V but with different edge sets [Formula omitted]. Informally, a function [Formula omitted] is smooth with respect to [Formula omitted] if [Formula omitted] whenever [Formula omitted]. We study the problem of understanding whether there exists a nonconstant function that is smooth with respect to all graphs in [Formula omitted], simultaneously, and how to find it if it exists.
Author(s): Ronald R. Coifman [sup.1] , Nicholas F. Marshall [sup.2] , Stefan Steinerberger [sup.3] Author Affiliations: (1) grid.47100.32, 0000000419368710, Department of Mathematics, Yale University, , New Haven, CT, USA (2) [...]