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OP-11904Status unassessedGraph theory

Induced Disjoint Paths without an H3 subgraph

Induced Disjoint Paths without an H3 subgraph. 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 Induced Disjoint Paths without an H3 subgraph. https://drops.dagstuhl.de/storage/04dagstuhl-reports/volume15/issue01/25041/DagRep.15.1.105/DagRep.15.1.105.pdf#page=14 Not an author-supplied code.

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

Fix the number kk of prescribed terminal pairs. Determine the complexity of finding kk mutually induced vertex-disjoint paths connecting the pairs in graphs with no H3H_3 subgraph. Here HiH_i consists of two disjoint three-vertex paths whose middle vertices are joined by a path of length ii.

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

Progress & source assessment

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).; Induced Disjoint Paths without an H3 subgraph linkCC BY 4.0; attributed editorial adaptation of the named section authors.

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