OpenFrontiers
Join
← Back to the index
OP-11900Status unassessedGraph theory

Atoms versus nonsimplicial connected graphs

Atoms versus nonsimplicial connected graphs. 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 Atoms versus nonsimplicial connected graphs. https://drops.dagstuhl.de/storage/04dagstuhl-reports/volume15/issue01/25041/DagRep.15.1.105/DagRep.15.1.105.pdf#page=12 Not an author-supplied code.

Source question · editorial summaryAs of 2025; current status unassessedSource & evidence ↓
Read original source ↗ 0Submit progressLean 4 ↓Discussion (0)

Problem statement

For a hereditary class G\mathcal G, let Gac\mathcal G_{ac} consist of its connected graphs with no clique cutset, and let Gsc\mathcal G_{sc} consist of its connected graphs that are complete or have no simplicial vertex. Does a natural problem Π\Pi exist that is polynomial-time solvable on G\mathcal G exactly when it is on Gsc\mathcal G_{sc}, for every G\mathcal G, but is NP-hard on some class F\mathcal F while polynomial-time solvable on Fac\mathcal F_{ac}?

Lean 4

Not yet attached

No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.

Share a formalization →Verification guide ↗

Background

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).; Atoms versus nonsimplicial connected graphs linkCC BY 4.0; attributed editorial adaptation of the named section authors.

Recorded progress

Add yours →

Nothing recorded yet. A pointer to a paper the entry is missing counts.

Machine attempts

0 recorded

Attempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.

No machine attempts recorded.

Sign in to run an attempt. New accounts start with enough credits for ten.

Discussion

0 notes

Notes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.

No notes yet.

Sign in to add a note.