  Syntax has been shown to benefit Coreference Resolution from incorporating
long-range dependencies and structured information captured by syntax trees,
either in traditional statistical machine learning based systems or recently
proposed neural models. However, most leading systems use only dependency
trees. We argue that constituent trees also encode important information, such
as explicit span-boundary signals captured by nested multi-word phrases, extra
linguistic labels and hierarchical structures useful for detecting anaphora. In
this work, we propose a simple yet effective graph-based method to incorporate
constituent syntactic structures. Moreover, we also explore to utilise
higher-order neighbourhood information to encode rich structures in constituent
trees. A novel message propagation mechanism is therefore proposed to enable
information flow among elements in syntax trees. Experiments on the English and
Chinese portions of OntoNotes 5.0 benchmark show that our proposed model either
beats a strong baseline or achieves new state-of-the-art performance. (Code is
available at https://github.com/Fantabulous-J/Coref-Constituent-Graph)
