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[잡담] 홀수점 홀수개가
Plum 2020.11.14 02:48 조회 371
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  •  
    아인수타인 Lv.12 2020.11.14 02:58

    아무렇게나 그래프를 그리면, 항상 선 하나당 점이 양끝에하나씩, 총 2개가 있게 됩니다. 그런데 각 점에 연결된 선의 개수(이것을 '차수'라고 합니다)를 세 줍시다. 그리고서 그것들을 전부 다 더하면 어떻게 될까요? 각 선을 양쪽에서 한 번씩 세 주니까 전체 선 개수의 2배가 나오겠죠? 그러니까 아래 그림처럼 세 준다고 생각하면 왜 그런지 이해하실 수 있을 겁니다.

    따라서, 각 점의 차수를 전부 더하면 전체 선 개수의 2배가 됩니다(이를 악수정리라고 하죠). 그런데 홀수점이 홀수 개라면 각 점의 차수를 전부 다 더한 것은 홀수인데, 이게 전체 선 개수의 2배가 될 수 있나요? 아니죠? 따라서, 항상 홀수점은 짝수 개가 됩니다.

    댓글 작성하기 좋아요0 댓글수1
    •  
      Plum Lv.7 2020.11.14 08:55

      !!

      좋아요0
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