Introduces spectral inducibility of graphs and proves a multipartite reduction for the extremal graphs when the target graph F is complete multipartite, with the leading asymptotic equal to ordinary inducibility.
Liu, Spectral generalized Tur ´an problems
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The kK_{r+1}-free n-vertex graph with maximum t-clique spectral radius is K_{k-1} joined to T_r(n-k+1) for sufficiently large n.
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The spectral inducibility of graphs
Introduces spectral inducibility of graphs and proves a multipartite reduction for the extremal graphs when the target graph F is complete multipartite, with the leading asymptotic equal to ordinary inducibility.
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Generalized spectral Tur\'an problems for disjoint cliques
The kK_{r+1}-free n-vertex graph with maximum t-clique spectral radius is K_{k-1} joined to T_r(n-k+1) for sufficiently large n.