How to reduce 3-COLOR to 42-COLOR?











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The requirement is that two adjacent vertices have different colors, and max. 42 colors.



I show that $ text{42-COLOR} $ is in NP and then I must reduce it from $ text{3-COLOR} $. Here it becomes complicated.



Is it similar to $ ktext{-COLOR} $ for any $k$?






graphs graph-theory np-complete reductions colorings







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  • Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
    – Juho
    6 hours ago










  • The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
    – gil
    5 hours ago















up vote
1
down vote

favorite












The requirement is that two adjacent vertices have different colors, and max. 42 colors.



I show that $ text{42-COLOR} $ is in NP and then I must reduce it from $ text{3-COLOR} $. Here it becomes complicated.



Is it similar to $ ktext{-COLOR} $ for any $k$?






graphs graph-theory np-complete reductions colorings







share|cite|improve this question









New contributor




gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
    – Juho
    6 hours ago










  • The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
    – gil
    5 hours ago













up vote
1
down vote

favorite









up vote
1
down vote

favorite











The requirement is that two adjacent vertices have different colors, and max. 42 colors.



I show that $ text{42-COLOR} $ is in NP and then I must reduce it from $ text{3-COLOR} $. Here it becomes complicated.



Is it similar to $ ktext{-COLOR} $ for any $k$?






graphs graph-theory np-complete reductions colorings







share|cite|improve this question









New contributor




gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











The requirement is that two adjacent vertices have different colors, and max. 42 colors.



I show that $ text{42-COLOR} $ is in NP and then I must reduce it from $ text{3-COLOR} $. Here it becomes complicated.



Is it similar to $ ktext{-COLOR} $ for any $k$?






graphs graph-theory np-complete reductions colorings




graphs graph-theory np-complete reductions colorings






share|cite|improve this question









New contributor




gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









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edited 3 hours ago









xskxzr

3,3671730




3,3671730






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asked 6 hours ago









gil

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62




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gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor





gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






gil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
    – Juho
    6 hours ago










  • The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
    – gil
    5 hours ago


















  • Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
    – Juho
    6 hours ago










  • The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
    – gil
    5 hours ago
















Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
6 hours ago




Do you want to reduce 42-COLOR to 3-COLOR, or the other way around?
– Juho
6 hours ago












The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
5 hours ago




The other way around. $ 3-COLOR propto 42-COLOR $. Now i noticed my mistake.
– gil
5 hours ago










1 Answer
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For an instance of 3-COLOR, try to add a complete graph of size $k-3$, and add an edge between each new vertex and each old vertex. Now you can prove the new graph is $k$-colorable iff the old graph is 3-colorable.






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    For an instance of 3-COLOR, try to add a complete graph of size $k-3$, and add an edge between each new vertex and each old vertex. Now you can prove the new graph is $k$-colorable iff the old graph is 3-colorable.






    share|cite|improve this answer

























      up vote
      3
      down vote













      For an instance of 3-COLOR, try to add a complete graph of size $k-3$, and add an edge between each new vertex and each old vertex. Now you can prove the new graph is $k$-colorable iff the old graph is 3-colorable.






      share|cite|improve this answer























        up vote
        3
        down vote










        up vote
        3
        down vote









        For an instance of 3-COLOR, try to add a complete graph of size $k-3$, and add an edge between each new vertex and each old vertex. Now you can prove the new graph is $k$-colorable iff the old graph is 3-colorable.






        share|cite|improve this answer












        For an instance of 3-COLOR, try to add a complete graph of size $k-3$, and add an edge between each new vertex and each old vertex. Now you can prove the new graph is $k$-colorable iff the old graph is 3-colorable.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 3 hours ago









        xskxzr

        3,3671730




        3,3671730






















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