Extremal parameters for graph families

Determine bounds or exact values for the clique number ω(Γ_t(G)) and independence number α(Γ_t(G)) of the spanning tree t-disjointness graph for interesting families of graphs G.

Background

The generalized graph Γ_t(G) provides a framework for studying pairwise intersection and disjointness among spanning trees of arbitrary graphs. Beyond computational complexity, the authors explicitly leave open the task of obtaining quantitative bounds or exact formulas for these parameters on meaningful graph classes.