For every fixed t, L_t ∪ {S_t,t,t,K_t,t}-free n-vertex graphs have tree independence number O(log^4 n).
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Tree independence number V. Walls and claws
For every fixed t, L_t ∪ {S_t,t,t,K_t,t}-free n-vertex graphs have tree independence number O(log^4 n).