Note
Every tree contains a large induced subgraph with all degrees odd

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Abstract

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.

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