Abstract
A hexagonal system is a finite 2-connected plane graph in which every interior face is bounded by a regular hexagon. A coronoid system is obtained from a hexagonal system by deleting some interior vertices and/or interior edges such that a unique interior face which is bounded by a polygon with more than six edges emerges, and each edge on the outer perimeter belongs to a hexagon. In this paper, a necessary and sufficient condition is given for a coronoid system to have perfect matchings. Moreover, a criterion is established for those coronoid systems with perfect matchings that possess some edges which do not belong to any perfect matching.
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