In this talk we discuss some problems related to finding large induced subgraphs of a given graph G which satisfy some degree-constraints (for example, all degrees are odd, or all degrees are j mod k, etc). We survey some classical results, present some interesting and challenging problems, and sketch solutions to some of them. This is based on joint works with Michael Krivelevich, and with Liam Hardiman and Michael Krivelevich.

# Odd subgraphs are odd (Asaf Ferber, UC Irvine)

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