Examples of extremal

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This leads to a picture of extremal combinatorics as a huge rag-bag of results with no connecting themes.
Knowing that we can use symmetry reduction to find the extremal solutions with reduced computational cost, we want to estimate the improvement.
Instead, the rivals fight preventively to evade the danger of reversion to a self-defeating extremal equilibrium that involves no further fighting.
Moreover, the extremal families are unique up to isomorphism.
This pins down the sought-after extremal trajectory uniquely.
We are also interested in extremal sampling, achieved by following a leftmost (or a rightmost) path.
In this paper our primary aim is to prove an exact form of this and describe the corresponding extremal structures.
The method for analysing their solvability is based on analytical properties of generalized acoustic potentials and the theory of extremal problems.
However, the results we obtain are weaker than in the previous sections, in the absence of similar results on the existence of systolically extremal metrics.
We now only need to show that the left extremal point of this island is trivial.
Many other theorems in extremal set theory provide such elegant characterizations of the largest possible family of sets given certain information on their intersections.
Moreover, the biclique on n/2 plus n/2 vertices is the 2 only extremal graph for this problem.
Nevertheless, players behaving according to extremal equilibria engage in rounds of costly war to reach a mutually acceptable bargain that is already in plain sight.
They are infinite-dimensional analogues of the inverse extremal problems relevant to the active minimization of sound fields in regular acoustic waveguides.
One is the possibility of applying purely combinatorial methods to certain extremal problems in additive number theory.
Having thus properly set the stage, we are in a position to formulate the extremal problem in which we are interested.

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