Improved asymptotic upper bound for universal graphs of spanning trees

Determine whether there exists a constant c < 14/(3 ln 3) such that the minimum number s^*(n) of edges in a graph containing every n-vertex tree as a subgraph satisfies s^*(n) ≤ (c + o(1)) n ln n.

Background

The paper defines s^*(n) as the minimum number of edges in a graph that contains all n-vertex trees as subgraphs, and establishes the upper bound s^*(n) ≤ s(n) ≤ (14/3)n log₃ n + O(n), equivalent to an asymptotic coefficient 14/(3 ln 3) when logarithms are natural.

The paper also proves a lower bound of n ln n − O(n) ≤ s^*(n). Thus, the authors explicitly ask whether the coefficient in their upper bound can be reduced below 14/(3 ln 3), which would narrow the gap between the known lower and upper bounds.