Sabidussi's Compatibility Conjecture
Statement
Can the edges of a finite connected multigraph, given a closed eulerian trail, be partitioned into circuits so that no circuit contains two edges used consecutively in the trail? The proof in fact four-colours the edges to satisfy the constraints.
Context
An old named conjecture in structural graph theory.
People
Attempts
No person has examined this. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.
Developed with GPT-5.6 Pro and GPT-5.6 Sol; the author reviewed the proof.
Reviews
1 machine checkNo person has reviewed this attempt. 1 machine check below — a machine check is not human verification.
Machine check · not human verification
machine: correctscope Lean formalization of the result
Lean 4 formalization available in the author's repository, alongside the arXiv preprint.
No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.
Discussion of this attempt
no comments
Solve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.
Discussion
Nothing has been said about this problem yet.
Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.