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The Grammar According to West By D.B. West 5. Expressions as units. There exists i < j with xi = xj . ( Double-Duty Definition of i, not OK ) There exists i such that i < j and xi = xj . The number of nonneighbors is n-1-d(u) i. The number of nonneighbors is n-1-d(u), which is at least i. The number of nonneighbors is n-1-d(u), which is greater than or equal to i. 5. Expressions as units. Exceptions Choose x V(G) such that x has minimum degree, in (is not a verb, OK) Let G' = G - x. (OK) equal (is a verb) Let G' = G - x be so-and-so. (not OK) 5. Expressions as units. Include each vertex independently with probability p=(ln n)/n. ( not OK ) Include each vertex independently with probability p, where p=(ln n)/n. ( OK ) 6. Separation of formulas. For x<0, x2 >0. ( not OK ) For x<0, it follows that x2 >0. ( OK ) For x<0, we have x2 >0. ( OK ) When k=2, G is Eulerian. ( not OK ) When k=2, the graph G is Eulerian. ( OK ) 6. Separation of formulas. For every bipartite graph G, χ(G) 2. ( not OK ) If G is bipartite, then χ(G) 2. ( OK ) 7. Initial notation. G is so-and-so. ( not OK ) The graph G is so-and-so. ( OK ) Let G be so-and-so. ( OK ) Suppose G is so-and-so. ( OK ) 8. Lists of size 2. Let x,y be vertices in G. ( not OK ) My friends John, Mary came to dinner. ( not OK ) Let x and y be vertices in G. (OK ) My friends John and Mary came to dinner. ( OK ) 8. Lists of size 2. Since a|b and a,b are maximal and minimal, ( not OK ) Since a|b, with a maximal and b minimal, ( OK ) If x , y are adjacent, ( not OK ) If x and y are adjacent, ( OK ) If {x,y} is a pair of adjacent vertices, ( OK ) 8. Lists of size 2. Exceptions. Let x,y,z be the vertices of T, ( OK ) Let {x,y,z} be the vertex set of T, ( OK, more precise ) Let {x,y,z} be a vertex set of T, go to school, go to a school, go to the school, go to church, go to a church, go to the church 8. Lists of size 2. Exceptions. Choose x,y V(G). ( OK ) For n,m 2, ( not OK ) For n 2 and m 2, ( OK ) For n and m 2, ( not OK ) Suppose n and m are greater than or equal to 2, ( OK ) 9. Parenthetic or wordless restrictions. Let m(m n) be the size. ( not OK ) Let m be the size where m n. ( OK ) Suppose there is an edge xy (≠e) in G such that… ( not OK ) Suppose there is an edge xy≠e in G such that… ( not OK, Double-Duty Definition ) Suppose that G has an edge xy other than e such that … ( OK ) 9. Parenthetic or wordless restrictions. For k m (k even), ( not OK ) For k m, k even, ( not OK ) For k m with k even, ( OK ) Consider ai (1 i n), ( not OK ) Consider ai for 1 i n, ( OK )