Placing Specified Vertices at Precise Locations on a Hamiltonian Cycle
Graphs and Combinatorics
Sharp minimum degree and degree sum conditions are proven for the existence of a Hamiltonian cycle passing through specified vertices with prescribed distances between them in large graphs.
Gould, Ronald, Colton Magnant, Pouria Salehi Nowbandegani.
"Placing Specified Vertices at Precise Locations on a Hamiltonian Cycle."
Graphs and Combinatorics, 33 (2): 369-385.