设 G(A_1,A_2;E)是以(A_1,A_2)为2分划的2连通的2部图.D(u)={v|v∈V(G),d(u,v)=2};δ_0=min{max{d(u),d(v)}|u,v∈V(G)且 d(u,v=2};D(δ_0)={u|u∈V(G)且d(u)≥δ_0};δ~*为 G 中某一项点度且δ~*≥δ_0,当δ~*>δ_0时δ~*还满足:(i)...设 G(A_1,A_2;E)是以(A_1,A_2)为2分划的2连通的2部图.D(u)={v|v∈V(G),d(u,v)=2};δ_0=min{max{d(u),d(v)}|u,v∈V(G)且 d(u,v=2};D(δ_0)={u|u∈V(G)且d(u)≥δ_0};δ~*为 G 中某一项点度且δ~*≥δ_0,当δ~*>δ_0时δ~*还满足:(i)δ~* 尽可能的大,(ü)对 Vu∈D(δ_0)及 D~*(u)={v|v∈(D(u)U{u}),d(v)<δ~*}有|D~*(u)|<d(u)。本文证明:(i)c(G)≥min{2|A_1|,2|A_2|,2(δ~*+δ_0)-4};(ü)当|A_1|=|A_2|,δ~*+δ_0≥|A_1|+1时 G 为 H 图.展开更多
文摘设 G(A_1,A_2;E)是以(A_1,A_2)为2分划的2连通的2部图.D(u)={v|v∈V(G),d(u,v)=2};δ_0=min{max{d(u),d(v)}|u,v∈V(G)且 d(u,v=2};D(δ_0)={u|u∈V(G)且d(u)≥δ_0};δ~*为 G 中某一项点度且δ~*≥δ_0,当δ~*>δ_0时δ~*还满足:(i)δ~* 尽可能的大,(ü)对 Vu∈D(δ_0)及 D~*(u)={v|v∈(D(u)U{u}),d(v)<δ~*}有|D~*(u)|<d(u)。本文证明:(i)c(G)≥min{2|A_1|,2|A_2|,2(δ~*+δ_0)-4};(ü)当|A_1|=|A_2|,δ~*+δ_0≥|A_1|+1时 G 为 H 图.
基金Supported by National Natural Science Foundation of China(No.11071002)Program for New Century Excellent Talents in University,Key Project of Chinese Ministry of Education(No.210091)+4 种基金Specialized Research Fund for the Doctoral Program of Higher Education(No.20103401110002)Science and Technological Fund of Anhui Province for Outstanding Youth(No.10040606Y33)National Science Foundation of the Department of Education of Anhui Province(Nos.KJ2011A195,KJ2010B136)Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University(No.KJJQ1001)Project for Academic Innovation Team of Anhui University(No.KJTD001B)
