Every n-vertex tree with maximum degree at most cn has Ramsey number max{t1 + 2t2, 2t1} - 1, where t1 >= t2 are the sizes of its bipartition classes.
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Ramsey numbers of trees
Every n-vertex tree with maximum degree at most cn has Ramsey number max{t1 + 2t2, 2t1} - 1, where t1 >= t2 are the sizes of its bipartition classes.