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As my first math project, I have been working on Sheehan's Conjecture and am stuck for weeks. I wonder if I am at a dead end. Sheehan's Conjecture states that every Hamiltonian 4-regular simple graph ...

What is the asymptotic probability that $G$ has a Hamilton cycle if $G$ is a random $n$ vertex $\frac{4}{3}n$ edge graph, with minimum degree 2 and without degree 2 vertices at distance 1 or 2 to each ...

Take the traveling salesman problem, but with three slight twists: You can choose a different start vertex for each of the two algorithms. Each path from one vertex to another is of unique, arbitrary ...