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OALib Journal期刊
ISSN: 2333-9721
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较大亏格曲面嵌入图的线性荫度
Keywords: 线性荫度,曲面,嵌入图,欧拉示性数
Abstract:
通过度再分配的方法研究嵌入到曲面上图的线性荫度.给定较大亏格曲面\,$\Sigma$\,上嵌入图\,$G$,如果最大度\,$\Delta(G)\geq(\sqrt{45-45\varepsilon}+10)$\,且不含\,4-圈,则其线性荫度为\,$\lceil\frac{\Delta}{2}\rceil$,其中若\,$\Sigma$\,是亏格为\,$h(h>1)$\,的可定向曲面时$\varepsilon=2-2h$,若\,$\Sigma$\,是亏格为\,$k(k>2)$\,的不可定向曲面时$\varepsilon=2-k$.改进了吴建良的结果,作为应用证明了边数较少图的线形荫度.
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