Abstract
We prove that the only obstacle for the graph of all linear extensions of a poset, consisting of two disjoint odd chains, to have a Hamilton cycle are the two vertices of degree 1. In other words, if these two vertices are removed, the remaining graph has a Hamilton cycle. This is equivalent to the statement, that there exists a Hamilton cycle in the subgraph G( k, l⧹{0 k 1 l , 1 l 0 k } of G( k, l), where G( k, l) is the graph of all binary ( k + l)-tuples containing k zeroes and l ones.
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