Degree sum conditions for Hamiltonicity on \(k\)-partite graphs (Q1376071)

This paper provides a result on the Hamiltonicity of a balanced \(k\)-partite graph of order \(kn\) in terms of degree sums of each pair of nonadjacent vertices in different parts. That shows if the sum is greater than \((k-2/(k+1))n\), when \(k\equiv 1\pmod 2\), and \((k-4/(k+2))n\), when \(k\equiv 0\pmod 2\), then the graph is Hamiltonian.