图的上可嵌入性与独立顶点的新度和

Up-Embeddability of Graphs with New Degree-Sum of Independent Vertices

中文关键词:  上可嵌入性  最大亏格  独立集.

英文关键词:up-embeddability  maximum genus  independent set.

中文摘要:

      令$k$($k\leq 3$)-边连通简单图$G$的最小度$\geq3$, 围长为$g$, $r=\lfloor\frac{g-1}{2}\rfloor$.对图$G$中任意的独立集$\{a_1,a_2,\cdots,a_{6/(4-k)}\}$， 若$$\sum_{i=1}^{6/(4-k)}d_G(a_i)>\frac{(4-k)\nu(G)-6(g-2r-\lfloor\frac{k}{3}\rfloor)}{(4-k)(2^r-1)(g-2r)}+\frac{6}{(4-k)}(g-2r-1),$$则图$G$是上可嵌入的.

英文摘要:

      Let $G$ be a $k$($k\leq 3$)-edge connected simple graph with minimal degree $\geq3$, girth $g$, $r=\lfloor\frac{g-1}{2}\rfloor$. For any independent set $\{a_1,a_2,\ldots,a_{6/(4-k)}\}$ of $G$, if $$ \sum_{i=1}^{6/(4-k)}d_G(a_i)>\frac{(4-k)\nu(G)-6(g-2r-\lfloor\frac{k}{3}\rfloor)}{(4-k)(2^r-1)(g-2r)}+\frac{6}{(4-k)}(g-2r-1), $$ then $G$ is up-embeddable.