The problem Monochomatic-Subgraph-Avoidance takes as input two undirected graphs F and G. It asks where F can be colored with two colors (say, red and blue) that does not contain a monochomatic (all-red or all-blue) G as a subgraph. (Note that when G has two nodes and one edge between them, this is equivalent to the 2-coloring problem of asking whether F can be colored so that no neighbors have the same color.) Next, show that Monochomatic-Subgraph-Avoidance is contained in one of the classes in the second level of the polynomial hierarchy.  ALso provide an expression using quantifiers

Database System Concepts
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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The problem Monochomatic-Subgraph-Avoidance takes as input two undirected graphs F
and G. It asks where F can be colored with two colors (say, red and blue) that does not contain
a monochomatic (all-red or all-blue) G as a subgraph. (Note that when G has two nodes and one
edge between them, this is equivalent to the 2-coloring problem of asking whether F can be colored
so that no neighbors have the same color.)

Next, show that Monochomatic-Subgraph-Avoidance is contained in one of the classes in
the second level of the polynomial hierarchy. 

ALso provide an expression using quantifiers

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