  A plane near-triangulation G can be decomposed into a collection of induced
subgraphs, described here as the W-components of G, such that G is perfect
(respectively, chordal) if and only if each of its W-components is perfect
(respectively, chordal). Each W-component is a 2-connected plane
near-triangulation, free of edge separators and separating triangles. Graphs
satisfying these conditions will be called W-near-triangulations. A linear time
decomposition of G into its W-components is achievable using known techniques
from the literature. W-near-triangulations have the property that the open
neighbourhood of every internal vertex induces a cycle. It follows that a
W-near-triangulation H of at least five vertices is non-chordal if and only if
it contains an internal vertex. This yields a local structural characterization
that a plane near-triangulation G is chordal if and only if it does not contain
an induced wheel of at least five vertices. For W-near-triangulations that are
free of induced wheels of five vertices, we derive a similar local criteria,
that depends only on the neighbourhoods of individual vertices and faces, for
checking perfectness. We show that a W-near-triangulation H that is free of any
induced wheel of five vertices is perfect if and only if there exists neither
an internal vertex x, nor a face f such that, the neighbours of x or f induces
an odd hole. The above characterization leads to a linear time algorithm for
determining perfectness of this class of graphs.
