How to use vue to determine the class of dom

<p class="chose-ck" v-for="(item,index2) in colors" :key="index2" ref="chosebox">
                  <p>{{item.name}}</p>
                  <dt v-for="(item2,index) in item.childsCurGoods" :key="item2.id" :class="index==iac[index2]?&#39;check&#39;:&#39;&#39;" :id="item2.id" :data-chosename="item.name" :data-choseidname="item2.name" :data-chose="item.id" :data-id="item2.id" @click="chek(index2,index)" >
                    {{item2.name}}
                  </dt>
                </p>js
  chek(index2, index) {
      this.iac[index2] = index
      this.iac = this.iac.concat([]);
      this.checkchose()
    },
    checkchose:function(){
      var chose=this
      var chosedom=chose.$refs.chosebox
      console.log(chosedom)
      for (var i=0;i<chosedom.length;i++) {
        var children=chosedom[i].children
        for (var j=0;j<children.length;j++) {  
          if(children[j].className=="check")
          {
            console.log(children[j])
          }
        }
      }
      
    }

if(children[j].className=="check")