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arXiv · 1803.10720

The edge-vertex inequality in a planar graph and a bipartition for the class of all planar graphs

M. R. Emamy-K.·Bahman Kalantari·Tatiana Correa
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Abstract

For a planar graph with a given f-vector $(f_{0}, f_{1}, f_{2}),$ we introduce a cubic polynomial whose coefficients depend on the f-vector. The planar graph is said to be real if all the roots of the corresponding polynomial are real. Thus we have a bipartition of all planar graphs into two disjoint class of graphs, real and complex ones. As a contribution toward a full recognition of planar graphs in this bipartition, we study and recognize completely a subclass of planar graphs that includes all the connected grid subgraphs. Finally, all the 2-connected triangle-free complex planar graphs of 7 vertices are listed.

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M. R. Emamy-K., Bahman Kalantari, Tatiana Correa. 2018-03-28. The edge-vertex inequality in a planar graph and a bipartition for the class of all planar graphs. https://arxiv.org/abs/1803.10720

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