In this paper, it is shown that for every maximal planar graph G=(V,E) , a strong embedding on some non orientable surface with genus at most |V(G)|-22 is admitted such that the surface dual of G is also a...In this paper, it is shown that for every maximal planar graph G=(V,E) , a strong embedding on some non orientable surface with genus at most |V(G)|-22 is admitted such that the surface dual of G is also a planar graph. As a corollary, an interpolation theorem for strong embeddings of G on non orientable surfaces is obtained.展开更多
The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover. Conversely, i...The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover. Conversely, it is not true. But for a 3-regular graph, the two conjectures are equivalent. In this paper, a characterization of graphs having a strong embedding with exactly 3 faces, which is the strong embedding of maximum genus, is given. In addition, some graphs with the property are provided. More generally, an upper bound of the maximum genus of strong embeddings of a graph is presented too. Lastly, it is shown that the interpolation theorem is true to planar Halin graph.展开更多
文摘In this paper, it is shown that for every maximal planar graph G=(V,E) , a strong embedding on some non orientable surface with genus at most |V(G)|-22 is admitted such that the surface dual of G is also a planar graph. As a corollary, an interpolation theorem for strong embeddings of G on non orientable surfaces is obtained.
基金the National Natural Sciences Foundation of China (No.10271048).
文摘The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover. Conversely, it is not true. But for a 3-regular graph, the two conjectures are equivalent. In this paper, a characterization of graphs having a strong embedding with exactly 3 faces, which is the strong embedding of maximum genus, is given. In addition, some graphs with the property are provided. More generally, an upper bound of the maximum genus of strong embeddings of a graph is presented too. Lastly, it is shown that the interpolation theorem is true to planar Halin graph.
