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
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).