Longest cycles in threshold graphs Original Research Article

The length of a longest cycle in a threshold graph is obtained in terms of a largest matching in a specially structured bipartite graph. It can be computed in linear time. As a corollary, Hamiltonian threshold graphs are characterized. This characterization yields Golumbicʹs characterization and sharpens Mintyʹs characterization. It is also shown that a threshold graph has cycles of length 3, …, l where l is the length of a longest cycle.