Uniquely hamiltonian graphs for many sets of degrees

Abstract

We give constructive proofs for the existence of uniquely hamiltonian graphs for various sets of degrees. We give constructions for all sets with minimum 2 (a trivial case), all sets with minimum 3 that contain an even number (for sets without an even number it is known that no uniquely hamiltonian graphs exist), and all sets with at least two elements and minimum 4 where all other elements are at least 10. For minimum degree 3 and 4, the constructions also give 3-connected graphs