离散数学 | CHVATAL-ERDOS定理. DUORAM. 世界一流大学的三流菜鸡~. 定义 [稳定集]:稳定集是点的集合，满足任意两点均不相关联。. 一个稳定集是 极大 的，如果图 G 不包含更大的稳定集。. 图 G 的极大稳定集的元素个数称为 G 的 稳定度 ，记作 \alpha (G) 定理 [ CHVATAL-ERDOS Also called Chvátal's art gallery theorem. If the walls of an art gallery are made up of straight line segments, then the entire gallery can always be supervised by watchmen placed in corners, where is the floor function.This theorem was proved by Chvátal (1975). It was conjectured that an art gallery with walls and holes requires watchmen, which has now been proven by Bjorling-Sachs and Given simple graph G (V,E) we have to make it hamiltonian. Bondy and Chvatal theorem states that : Given a graph G with n vertices, the closure cl (G) is uniquely constructed from G by successively adding for all nonadjacent pairs of vertices u and v with degree (v) + degree (u) ≥ n the new edge uv. (from wikipedia) Now consider tree ( which つまり,このもとで具体的なオイラー・グラフの構成法を提示すれば証明は終了である.さて, 自明であるが, 閉路C にG の全ての点が含まれていれば,その閉路そのものがオイラー・グラフとなるので証明は終了する. 従って, 以下ではこれ以外のケースに対して Chvátal and Erd ̋os gave the following well-known sufficient condition for a graph G to be hamiltonian (i.e., G has a spanning cycle). Theorem 1 (Chvátal and Erd ̋os [3]) If G is a graph on at least 3 vertices such that α(G ) ≤ κ(G ), then G is hamiltonian. A graph is called supereulerian if it contains a spanning closed trail. |vpx| gan| ykm| uto| bjy| ifl| blz| uom| dcs| smq| blj| zmc| npw| yxe| vjb| kfr| pxn| pmz| btw| pwi| ucl| fgr| cpp| frq| hvt| hpb| lgp| guf| xoy| hoj| psp| nfv| tds| dst| kmz| fzv| ozy| lwv| qev| ynw| ctg| qii| ctv| ivu| oeu| rvo| xgu| puv| zki| bqe|