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| A CHARACTERIZATION OF THE EMBEDDABILITY OFGRAPHS ON THE SURFACE OF GIVEN GENUS |
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Citation： |
Liu Ying,Liu Yanpei.A CHARACTERIZATION OF THE EMBEDDABILITY OFGRAPHS ON THE SURFACE OF GIVEN GENUS[J].Chinese Annals of Mathematics B,1996,17(4):457~462 |
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Net amount： 673 |
Authors： |
Liu Ying; Liu Yanpei |
Foundation： |
the National Natural Science Foundation of China |
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| Abstract： |
The embedding technique based on an operator appeared in [Liu, Y. P., Scientia Sinica, Special Issue on Math, 1(1979), 191-201 (in Chinese)] for determining the maximum non-orientable genus of a graph is developed to obtain the general theorem which presents a necessary and sufficient condition for a graph to be embeddable into either the orientable or the non-orientable surface of genus $k$. Furthermore, the greatest lower bound of the lengths of genus ranges of the class of nonplanar graphs which are up-embeddable is also obtained. |
Keywords： |
Double graph, Eulerian directed circuit, Orientable surface,
Embeddability |
Classification： |
05C10 |
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