Contents

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Computation of the Folkman Number Fv(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

Abstract

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