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2020•arXiv (Cornell University)Open access

Every graph contains a linearly sized induced subgraph with all degrees odd

Asaf Ferber, Michael Krivelevich

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Abstract

We prove that every graph $G$ on $n$ vertices with no isolated vertices contains an induced subgraph of size at least $n/10000$ with all degrees odd. This solves an old and well-known conjecture in graph theory.

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We prove that every graph $G$ on $n$ vertices with no isolated vertices contains an induced subgraph of size at least $n/10000$ with all degrees odd. This solves an old and well-known conjecture in graph theory.

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Available abstract

We prove that every graph $G$ on $n$ vertices with no isolated vertices contains an induced subgraph of size at least $n/10000$ with all degrees odd. This solves an old and well-known conjecture in graph theory.

Key concepts: Combinatorics, Factor-critical graph, Induced subgraph, Graph factorization, Conjecture, Induced subgraph isomorphism problem, Graph, Mathematics

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