Transcript The Grammar According to West

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 )