Brualdi's Question on Hamiltonicity of Interchange Graphs
Statement
The interchange graph has the -matrices with row sums and column sums as vertices, adjacent when they differ by a single interchange. Brualdi asked whether is always Hamiltonian. It satisfies more: it is maximally Hamiltonian, Hamilton-laceable when bipartite and Hamilton-connected when not.
Context
A long-standing question of Brualdi in combinatorial matrix theory, standard background for anyone working with interchange classes of 0-1 matrices.
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