feat(SimpleGraph): Weaker condition for paths in acyclic graphs#25630
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feat(SimpleGraph): Weaker condition for paths in acyclic graphs#25630
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`IsAcyclic.isPath_iff_chain'` defines a weaker condition for proving that a walk is a path, in particular it shows that rather than all vertices in the support of a walk being distinct, one must only show that consecutive vertices are distinct. This leads to a simple corollary that trails are paths in acyclic graphs.
PR summary b27d4790e1Import changes for modified filesNo significant changes to the import graph Import changes for all files
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This PR has been migrated to a fork-based workflow: #25814 |
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IsAcyclic.isPath_iff_chain'defines a weaker condition for proving that a walk is a path, in particular it shows that rather than proving that all vertices in the support of a walk are distinct, one must only show that consecutive edges are distinct (e.g. every other vertex must be distinct.) This leads to a simple corollary that trails are also paths in acyclic graphs.