The latter case happens if and only if there exists no Green function, or equivalently there exists no non-constant subharmonic function

bounded from above.

We prove that the game colouring number of the m-th power of a forest with maximum degree [DELTA] [greater than or equal to] 3 is

bounded from above by

t[right arrow][+ or -][infinity]] [phi](t) = -[infinity], [phi] is

bounded from above by a constant [beta] > 0, so f([bar.

m], all the eigenvalues are bigger than 1 and

bounded from above, if [lambda] = [[lambda].

k] (A) can be

bounded from above by a geometric quantity involving Z, namely a multiple of the [L.

Now (1) implies that the cumulative running time of recursive calls of procedure color in (C2) is

bounded from above by C [(n - 1).

Thus there must exist at least one random choice that yields a schedule whose value is

bounded from above by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Beta]], which is

bounded from above by unity since [Beta] [greater than] 0.

We record here the very simple inequalities between the relevant terms; for ease of notation, we use the symbol [nearly egual to] to mean the quantity on its left is

bounded from above and below by a constant, which is independent of z' [element of] U [intersection] [omega] and small [delta] > 0, times the quantity on its right.

3)

bounded from above by some fixed constant on some semicircles, whose radii tend to infinity.

1995]: the radius of the circumsphere is

bounded from above by a constant times the length of the shortest edge.

For isotropic meshes it is then

bounded from above by 1 (see Section 4).