In S_{t,t,t}-free graphs, deleting the closed neighborhoods of at most 3t+11 vertices yields a rigid extended strip decomposition whose particles each have at most half the total weight.
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Graphs with no long claws: An improved bound for the analog of the Gy\'{a}rf\'{a}s' path argument
In S_{t,t,t}-free graphs, deleting the closed neighborhoods of at most 3t+11 vertices yields a rigid extended strip decomposition whose particles each have at most half the total weight.