Abstract
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.
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Zhang, H. (2007). Regular Coronoids and Ear Decompositions of Plane Elementary Bipartite Graphs. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_28
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DOI: https://doi.org/10.1007/978-3-540-70666-3_28
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