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Published in:
2007 | OriginalPaper | Chapter
Regular Coronoids and Ear Decompositions of Plane Elementary Bipartite Graphs
Author : Heping Zhang
Published in: Discrete Geometry, Combinatorics and Graph Theory
Publisher: Springer Berlin Heidelberg
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A connected bipartite graph is called
elementary
(or
normal
) if its every edge is contained in some perfect matching. In
rho
classification of coronoids due to Cyvin et al., normal coronoids are divided into two types: regular and half essentially disconnected. A coronoid is called
regular
if it can be generated from a single hexagon by a series of normal additions of hexagons (modes
L
1
,
L
3
or
L
5
) plus corona condensations of hexagons of modes
L
2
or
A
2
. Chen and Zhang (1997) gave a complete characterization: A coronoid is regular if and only if it has a perfect matching
M
such that the boundaries of non-hexagon faces are all
M
-alternating cycles. In this article, a general concept for the regular addition of an allowed face is proposed and the above result is extended to a plane elementary bipartite graph some specified faces of which are forbidden by applying recently developed matching theory. As its corollary, we give an equivalent definition of regular coronoids as a special ear decomposition.