Classes of Upper Embeddable Graphs with Specific Minimum Degree-Sum of Vertices in Independent-Set(English)
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摘要: 结合边连通度,探讨了独立集中具有最小特定度和的点的上可嵌入图.得到了下列结果. (1)设G,是一个2-边连通简单图且满足条件:对任意一个G的3-独立集I, ∨xi ,xj ∈I (i,j = 1,2,3), d(xi ,xj)≧3 (1 ≦ i ≠ j ≦ 3) =∑i = 13 d(xi) ≧ v + 1(v = | V(G)|}), 则G是上可嵌入的;(2)设G是一个3-边连通简单图且满足条件:对任意一个G的6-独立集I, ∨xi ,xj ∈I (1≦i,j≦6), d(xi,xj) ≧3(1 ≦ i ≠ j ≦ 6) = ∑i = 16 d(xi) ≧ v + 1(v = | V(G)|), 则G是上可嵌入的.Abstract: Combined with the edge-connectivity, this paper investigated the upper embeddable graphs with specific minimum degree-sum of vertices in its independent-set, and obtained the following results. (1) Let G be a 2-edge-connected simple graph, if G satisfies the following conditions: for any 3-independent set I in G, ∨xi ,xj ∈I (i,j = 1,2,3), d(xi ,xj)≧3 (1 ≦ i ≠ j ≦ 3) =∑i = 13 d(xi) ≧ v + 1(v = | V(G)|}), then G is upper embeddable; (2) Let G be 3-edge-connected simple graph, if G satisfies the following conditions: for any 6-independent set I in G, ∨xi ,xj ∈I (1≦i,j≦6), d(xi,xj) ≧3(1 ≦ i ≠ j ≦ 6) = ∑i = 16 d(xi) ≧ v + 1(v = | V(G)|), then G is upper embeddable.
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