This is a true/false question I'm trying to solve to prepare for my exam. Could someone confirm my answer?
What I think: true, because the graph then has only even degrees and the graph is also cohesive (because of Hamilton cyclus).
2026-03-27 00:00:11.1774569611
Are all 4-regular Hamiltonian graphs Euler graphs?
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Yes, but this follows from the fact that every vertex has even degree i.e., the graph is $4$-regular, and that the graph is connected, from the fact that the graph is Hamiltonian. [All that is needed is every vertex even degree and the graph is connected.]