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Search options not deleted user 43954
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Relationship between minimum vertex cover and matching width

Your suspicion is correct. The following hypergraph $H$ provides a negative answer to your question. Let $V=\{0,1,\dots, 11\}$. Then $V=V_0\cup V_1\cup V_2$, where $V_0=\{0,1,2,3\}$, $V_1=\{4,5,6,7\}$ …
Alex Ravsky's user avatar
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