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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Computation of the Folkman Number \( F_{v}(3,5;6) \)

Zehui Shao1, Meilian Liang2, Lingiang Pan3, Xiaodong Xu4
1School of Information Science & Technology Chengdu University, Chengdu 610106, China; Key Laboratory of Pattern Recognition and Intelligent Information Processing
2School of Mathematics and Information Science Guangxi University, Nanning 530004, China
3Key Laboratory of Image Processing and Intelligent Control; Department of Control Science and Engineering Huazhong University of Science and Technology, Wuhan 430074, China
4Guangxi Academy of Sciences Nanning, Guangxi 530007, China
  • Published: 31/05/2012

Abstract

We prove that \( F_v(3,5;6) = 16 \), which solves the smallest open case of vertex Folkman numbers of the form \( F_v(3, k; k+1) \). The proof uses computer algorithms.

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Citation
Zehui Shao, Meilian Liang, Lingiang Pan, Xiaodong Xu. Computation of the Folkman Number \( F_{v}(3,5;6) \)[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 081. 11-17. DOI: .