All Questions

Let $G$ be a $3$-connected Hamiltonian graph with at least one edge that belongs to each H-cycle of $G$. Some authors (e.g. in the link given here) call such an edge an a-edge and an edge that belongs ...

I would like to know more about uniquely hamiltonian graphs with minimum vertex degree at least 3, and in particular what is the smallest one. (Recall that a graph is hamiltonian if it has a cycle ...

A graph is uniquely hamiltonian if it has exactly one hamiltonian cycle. According to a conjecture there are no $r$-regular uniquely hamiltonian graphs for $r > 2$ and of special interest is the ...

Question from 2013 gives one counterexample to Nash-Williams's conjecture about hamiltonicity of dense digraphs. Later, we found tens of counterexamples on more than 30 vertices and believe there are ...

Question from 2013 gives one counterexample to Nash-Williams's conjecture 1975 about hamiltonicity of dense digraphs. In the linked answer, @LouisD "reverse engineered" the counterexample ...