math.CO — Combinatorics
Contracting a pendant edge can increase the mean subtree order
Cambie, Jooken and Wagner conjectured that contracting an edge of a connected graph decreases the mean subtree order by at least 1/3, as it does for trees. We construct unicyclic graphs of order n and maximum degree 3 in which contracting a pendant edge increases the mean subtree order by n/450+O(1), disproving the conjecture. In this family the bound first fails at 481 vertices and contraction first increases the mean at 631 vertices.
Primarily AI-generated textHuman understanding: all partscounterexampleedge contractionmean subtree order