Heinig's question on spanning near-squares of odd cycles in Dirac graphs
For every odd integer , does every -vertex graph satisfying contain a spanning subgraph isomorphic to the graph obtained from the square of an -cycle by deleting every other edge on the cyclic periphery until exactly three consecutive vertices of the resulting graph have degree ? The question has two natural interpretations of which peripheral edges are deleted.
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Progress summary
A repository manuscript claims to refute Heinig’s question, but its counterexample has not been independently checked.
Heinig’s question asks whether the stated spanning near-square existence property holds for Dirac graphs. No proposer, date, or classical partial results were identified in the retrieved material.
September 2026 claimed counterexample
Alper Ferudun’s repository manuscript, Dirac Graphs Without a Spanning Near-Square of an Odd Cycle: A Negative Answer to a Question of Heinig, presents a construction claimed to refute the existence property. If valid, it would give a negative answer and settle the question, but the retrieved evidence supplies neither the construction nor an independent verification.
Current status (as of September 2026): A manuscript claims a counterexample that would settle Heinig’s question negatively, but the claim remains unverified.
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