Let G be a 3 edge connected graph (possibly with multiple edges or loops), and let γ M(G) and β(G) be the maximum genus and the Betti number of G, respectively. Then γ M(G)≥β(G)/3 can be proved and this...Let G be a 3 edge connected graph (possibly with multiple edges or loops), and let γ M(G) and β(G) be the maximum genus and the Betti number of G, respectively. Then γ M(G)≥β(G)/3 can be proved and this answers a question posed by Chen, et al. in 1996.F FIRST OR展开更多
In this paper we prove that the generalized permutation graph G（n, k） is upper embeddable if it has at most two odd subcycles, and that the maximum genus of G（n, k） is more than 「β（G（n,k））/3」 in most cases.
In this paper we mainly prove that let G be a(k+1)-edge-connected simple graph of order n with girth g.Then G is upper embeddable if for any independent set I(G) = {vi | 1 i k2 + 2},k = 0,1,2 and the lower bound is ti...In this paper we mainly prove that let G be a(k+1)-edge-connected simple graph of order n with girth g.Then G is upper embeddable if for any independent set I(G) = {vi | 1 i k2 + 2},k = 0,1,2 and the lower bound is tight.展开更多
A connected loopless graph that can be embedded on some (orientable or nonorientable) surface such that the size of each face does not exceed 5 is upper embeddable.
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,x_i,x_j∈I(i,j=1,2,3),d(x_i,x_j)≥3(1≤i≠j≤3)sum from i=1 to 3 d(x_i)≥v+1 (v=V...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,x_i,x_j∈I(i,j=1,2,3),d(x_i,x_j)≥3(1≤i≠j≤3)sum from i=1 to 3 d(x_i)≥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,x_i,x_j∈I(i,j=1,2,3,4,5,6),d(x_i,x_j)≥3(1≤i≠j≤6)sum from i=1 to 6 d(x_i)≥v+1(v=|V(G)|),则G是上可嵌入的.展开更多
文摘Let G be a 3 edge connected graph (possibly with multiple edges or loops), and let γ M(G) and β(G) be the maximum genus and the Betti number of G, respectively. Then γ M(G)≥β(G)/3 can be proved and this answers a question posed by Chen, et al. in 1996.F FIRST OR
基金The NSF (10671073) of Chinathe Scientific Fund (03080045) of the Gathered Talents by Nantong UniversityNSF (07KJB110090) of Jiangsu University.
文摘In this paper we prove that the generalized permutation graph G（n, k） is upper embeddable if it has at most two odd subcycles, and that the maximum genus of G（n, k） is more than 「β（G（n,k））/3」 in most cases.
文摘In this paper we mainly prove that let G be a(k+1)-edge-connected simple graph of order n with girth g.Then G is upper embeddable if for any independent set I(G) = {vi | 1 i k2 + 2},k = 0,1,2 and the lower bound is tight.
文摘A connected loopless graph that can be embedded on some (orientable or nonorientable) surface such that the size of each face does not exceed 5 is upper embeddable.
基金Supported by the National Natural Science Foundation of China(10271048)and Shanghai Priority Academic Discipline and Sci-ence and Technology Commission of Shanghai Municipality(04JC14031).
文摘结合边连通度,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,x_i,x_j∈I(i,j=1,2,3),d(x_i,x_j)≥3(1≤i≠j≤3)sum from i=1 to 3 d(x_i)≥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,x_i,x_j∈I(i,j=1,2,3,4,5,6),d(x_i,x_j)≥3(1≤i≠j≤6)sum from i=1 to 6 d(x_i)≥v+1(v=|V(G)|),则G是上可嵌入的.
