次和σ_2(G)条件与图的链划分

A DEGREE SUM σ 2(G) CONDITION OF PATH PARTITION IN CONNECTED GRAPH

证明了满足σ２ （ Ｇ）≥ｎ－ π（ Ｇ）的连通图 Ｇ，当图 Ｇ的阶为ｎ＝ ｎ１ ＋ ｎ２ ＋ …＋ ｎｐ 且ｎ１，ｎ２，…，ｎｐ 中奇数个数≥π（ Ｇ）时，存在阶为ｎ１，ｎ２，…，ｎｐ

If the order of the connected graph G that satisfied σ 2(G)≥n-π(G) is n=n 1+n 2+…+n p and the number of odd is more than or equal π(G) in n 1,n 2,…,n p,the path partition with order n 1,n 2,…,n p exist in graph G can be proved.