Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, April 27, 2021, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Michael Krivelevich (Tel Aviv University)

Linearly sized induced odd subgraphs

A classical result of Gallai from the sixties asserts that the vertex set V of every graph G can be partitioned into two parts V_1, V_2, each spanning an induced subgraph with all degrees even. It follows that every n-vertex graph contains an induced subgraph on at least n/2 vertices with even degrees.

What can be said about the odd case? A decades old conjecture suggested that every graph G on n vertices of positive minimum degree contains a subset V_0 of size linear in n, with all degrees in the induced subgraph G[V_0] being odd.

Recently, in a joint work with Asaf Ferber we managed to prove this conjecture. In this talk I will discuss the problem and main ingredients of the proof.

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