/sci/ - Science & Math

Is this graph Hamiltonian, with each VERTEX being visited exactly once, on an open walk/trail/path? It's a representation of a puzzle game level which, If I've interpreted and modeled everything correctly, must be Hamiltonian. I keep getting stuck, with multiple vertices left out. 43 vertices, 57 edges. Any useful properties/lemmas here?

If anyone cares to look, the level is #14 in this. https://armorgames.com/connecty-game/18884?fp=ng Tedious to load and skip levels, but you can arrow to the level after a few minutes. The level also does have an extra condition on certain locked tiles/vertices and previous steps, but I ignore that for the purpose of the present question.