Discoveries / combinatorics

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.