K_t-minor-free graphs embedding all planar n-graphs require exponential size while polynomial-sized minor-free universal graphs exist for trees and K4-minor-free graphs as induced subgraphs.
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Faithful universal graphs for minor-closed classes
K_t-minor-free graphs embedding all planar n-graphs require exponential size while polynomial-sized minor-free universal graphs exist for trees and K4-minor-free graphs as induced subgraphs.