Cop number of 2K_2-free graphs

03/27/2019

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by   Vaidy Sivaraman, et al.

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We prove that the cop number of a 2K_2-free graph is at most 2 if it has diameter 3 or does not have an induced cycle of length k, where k ∈{3,4,5}. We conjecture that the cop number of every 2K_2-free graph is at most 2.