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How can I prove that this two statements are equivalent?



The 2019 Stack Overflow Developer Survey Results Are InDetermining the equivalence of two statementsExistence of a $k$-coloring of a complete graph with no monochromatic subgraphProve that every $k$-chromatic graph has size $mgeq binom k2 $Partition Of Graph's edges Into 3 GroupsProve that if |$V(G)$| is even then $alpha'(G)=frac V(G)2$How can I prove ($number of verticies over size of maximum independent set$ ) $leq$ chromatic number?How to prove G is a perfect matchingvertex coloring of a graph $G$ such that colors appear twiceProve that the even cycles are 2-list-colorable.4 color theorem equivalent to cubic planar bridgeless are 3 edge colorable










0












$begingroup$


Given: complete graph G and I a list assignment for G

prove:
G has proper coloring $Leftrightarrow $
$ forall ;Zsubseteq V(G)$ : $mid Z mid leq mid cup_zin Z; I(z) mid $



Can someone give me a hint how to solve it?










share|cite|improve this question









$endgroup$
















    0












    $begingroup$


    Given: complete graph G and I a list assignment for G

    prove:
    G has proper coloring $Leftrightarrow $
    $ forall ;Zsubseteq V(G)$ : $mid Z mid leq mid cup_zin Z; I(z) mid $



    Can someone give me a hint how to solve it?










    share|cite|improve this question









    $endgroup$














      0












      0








      0





      $begingroup$


      Given: complete graph G and I a list assignment for G

      prove:
      G has proper coloring $Leftrightarrow $
      $ forall ;Zsubseteq V(G)$ : $mid Z mid leq mid cup_zin Z; I(z) mid $



      Can someone give me a hint how to solve it?










      share|cite|improve this question









      $endgroup$




      Given: complete graph G and I a list assignment for G

      prove:
      G has proper coloring $Leftrightarrow $
      $ forall ;Zsubseteq V(G)$ : $mid Z mid leq mid cup_zin Z; I(z) mid $



      Can someone give me a hint how to solve it?







      graph-theory coloring






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Mar 30 at 11:30







      user659201



























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