Expected-dimension conjecture for subdividing an edge in a graph

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Let GG be a graph on n−1n-1 vertices, and let k→lk\to l be an edge in GG. Construct a graph G′G' on nn vertices by subdividing the edge k→lk\to l: add vertex nn and replace the edge k→lk\to l by the two edges k→nk\to n and n→ln\to l. Edge-subdivision conjecture. If GG has the expected dimension, then G′G' has the expected dimension as well. This conjecture proposes that expected dimension is preserved when an edge is subdivided; the preceding discussion gives a converse failure for a related construction, while the source does not specify a resolution of this conjecture.

References

Primary source

Jasmijn A. Baaijens and Jan Draisma, “On the existence of identifiable reparametrizations for linear compartment models”, arXiv:1509.02551 (2016).

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