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Vertex edge graphs

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OK so my friend asked me how to solve this question i didn't know how but tried anyway and got the right answer but i want to know if i did it correctly

6 boys are working on 5 go carts. each boy works on more than one cart. it takes one weekend to make one cart. there are 8 conflicts represented by edges on the vertex edge graph. how many weekends will it take?
the answer is 3
the graph looks like this

A
/ \ \
/ \ \
/ \ \
B----------\----/E
\ \ / /
\ /\ /
\ / \ /
\ / \ /
C-------D


now imagine the lines quite a bit straighter, but if you need a little help there are lines between

a-b
a-e
a-d
b-c
b-e
c-d
c-e
d-e

please tell me how to solve this problem correctly

  • Vertex edge graphs -

    OK ignore the graph the spaces didn't stay when i submitted it the verticies form a pentagon

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