Abstract
A node in the n -dimensional hypercube Q n is called an odd node (resp. an even node) if the sum of all digits of the node is odd (resp. even). Let F ⊂ E ( Q n ) and let L be a linear forest in Q n − F such that | E ( L ) | + | F | ≤ n − 2 for n ≥ 2 . Let x be an odd node and y an even node in Q n such that none of the paths in L has x or y as internal node or both of them as end nodes. In this note, we prove that there is a Hamiltonian path between x and y passing through L in Q n − F . The upper bound n − 2 on | E ( L ) | + | F | is sharp.
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