Note making a K 4-free graph bipartite

Abstract

We show that every K 4-free graph G with n vertices can be made bipartite by deleting at most n 2/9 edges. Moreover, the only extremal graph which requires deletion of that many edges is a complete 3-partite graph with parts of size n/3. This proves an old conjecture of P. Erdős.

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Correspondence to Benny Sudakov.

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Research supported in part by NSF CAREER award DMS-0546523, NSF grant DMS-0355497, USA-Israeli BSF grant, and by an Alfred P. Sloan fellowship.

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Sudakov, B. Note making a K 4-free graph bipartite. Combinatorica 27, 509–518 (2007). https://doi.org/10.1007/s00493-007-2238-0

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Mathematics Subject Classification (2000)

  • 05C35