中文摘要：

设α（G），β（G）和n（G）分别表示图G的独立数、匹配数和阶数．图的独立数和匹配数是图的两个较重要的参数．证明了对于不含三角形且最大度不超过5的图，独盘数、匹配数和阶数之间存在两个最优的数量关系．

英文摘要：

Let α（G）, β（G） and n（G） be the independence number, the matching number and the order of a graph G, respectively, the independence number and the matching number are two more important Parameters for a graph. In this paper, it is proved that there exist two optimal numerical relationships between them for the graphs which are K3-free and the maximum degree is 5 at most.