WOWII Conjecture 72: Two induced trees pin down tree($G$)

The evenly-divided reading of WOWII Conjecture 72 holds: $\lceil(A + L)/3\rceil \le t,$ where $t =$ tree($G$) (order of a largest induced tree), $A =$ average eccentricity and $L =$ maximum neighbourhood independence number. A stronger reading that divides only $L$ by three is false. The argument rests on two elementary observations (a diametral path is chordless and therefore induces a tree on $D+1$ vertices; a maximum independent set in a neighbourhood induces a star on $L+1$ vertices). The original conjecture’s precise wording is not yet pinned in a public formal repository, so statement fidelity remains to be audited.

The evenly-divided reading of WOWII Conjecture 72 holds: $\lceil(A + L)/3\rceil \le t,$ where $t =$ tree($G$) (order of a largest induced tree), $A =$ average eccentricity and $L =$ maximum neighbourhood independence number. A stronger reading that divides only $L$ by three is false. The argument rests on two elementary observations (a diametral path is chordless and therefore induces a tree on $D+1$ vertices; a maximum independent set in a neighbourhood induces a star on $L+1$ vertices). The original conjecture’s precise wording is not yet pinned in a public formal repository, so statement fidelity remains to be audited.