Spectral extrema for avoiding disjoint cycles of length at least six

Classify, for every sufficiently large number of vertices n and fixed integers t≥1 and ℓ≥6, the spectral extremal graphs among n-vertex 1-planar graphs containing no t pairwise vertex-disjoint copies of the cycle C_ℓ.

Background

The paper notes that for cycle lengths ℓ≥6, the interaction between the two dominating vertices produced by the K_{2,n-2}-reduction and long cycles is more complicated than in the C5 and 2C5 cases. In particular, copies of C_ℓ may arise from long paths and intricate local structures in the residual graph, so the component structures and corresponding spectral maximizers remain to be classified.