اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe edge-vertex inequality in a planar graph and a bipartition for the class of all planar graphs
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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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We initiate a systematic study of the fractional vertex-arboricity of planar graphs and demonstrate connections to open problems concerning both fractional coloring and the size of the largest induced forest in planar graphs. In particular, the follo
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