Every tree contains a large induced subgraph with all degrees odd

Caro et al. [3] proved that every tree of order n contains an induced subgraph of order at least ⌈n2⌉ with all degrees odd, and conjectured a better bound. In this note we prove that every tree of order n contains an induced subgraph of order at least 2⌊(n + sol1)3⌋ with all degrees odd; this bound is best possible for every value of n.