ex(n, B_t) is asymptotically between (1/(2√2) + o(1))√t n^{3/2} and (1/2 + o(1))√t n^{3/2}, with bipartite versions between (1/4 + o(1))√t n^{3/2} and (1/(2√2) + o(1))√t n^{3/2}, plus sharper constants for B_2 and a general tree bound.
307(2007), 3055–3062
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The Tur\'{a}n number of the Cartesian product of a star and an edge
ex(n, B_t) is asymptotically between (1/(2√2) + o(1))√t n^{3/2} and (1/2 + o(1))√t n^{3/2}, with bipartite versions between (1/4 + o(1))√t n^{3/2} and (1/(2√2) + o(1))√t n^{3/2}, plus sharper constants for B_2 and a general tree bound.