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OP-11899Status unassessedGraph theory

Edge-edit radius for sidestepping Hamiltonicity

Edge-edit radius for sidestepping Hamiltonicity. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

MSC 05C · Graph theoryMSC 68Q25 · Analysis of algorithms and problem complexity

Editorial MSC2020 mapping of Edge-edit radius for sidestepping Hamiltonicity. https://drops.dagstuhl.de/storage/04dagstuhl-reports/volume15/issue01/25041/DagRep.15.1.105/DagRep.15.1.105.pdf#page=11 Not an author-supplied code.

Source question · editorial summaryAs of 2025; current status unassessedSource & evidence ↓
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Problem statement

Given an nn-vertex graph GG, a sidestepping algorithm may return a graph JJ on the same vertices and correctly decide whether JJ has a Hamiltonian cycle. What is the smallest edge-edit radius d(n)d(n) permitting a polynomial-time algorithm with ∣E(G)△E(J)∣≤d(n)|E(G)\mathbin\triangle E(J)|\le d(n) for every input?

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Background

Editorial question summary. Consult the linked source for the complete model, assumptions and discussion.

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Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

References
  1. [1]Seminar 25041 problem-session contributors. Dagstuhl 25041 — Graph Classes and Algorithmic Complexity (2025).; Edge-edit radius for sidestepping Hamiltonicity linkCC BY 4.0; attributed editorial adaptation of the named section authors.

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