For all fixed k and all sufficiently large m, every m-edge graph with no k vertex-disjoint triangles has adjacency spectral radius at most (k-1)+sqrt(m-k(k-1)), with equality only for the join of K_{2k-1} with an independent set.
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A sharp fixed-size spectral bound for $kK_3$-free graphs
For all fixed k and all sufficiently large m, every m-edge graph with no k vertex-disjoint triangles has adjacency spectral radius at most (k-1)+sqrt(m-k(k-1)), with equality only for the join of K_{2k-1} with an independent set.