Extremal Graph Theory Djvu Format — http://bit.ly/2dofDRa

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Extremal Graph Theory Djvu Format

 

⌊ n 2 4 ⌋ {displaystyle leftlfloor {frac {n^{2}}{4}}rightrfloor } . Specifying a large minimum degree removes the objection that there may be a few ‘pathological’ vertices; if the minimum degree of a graph G is 1, for example, then there can be no isolated vertices (even though G may have very few edges). Instead of cliques, if the same question is asked for complete multi-partite graphs, the answer is given by the ErdsStone theorem. Density results[edit]. Contents 1 Examples 2 History 3 Density results 4 Minimum degree conditions 5 See also 6 Notes 7 References . What is the maximum possible number of edges in an undirected graph G with n vertices which does not contain K3 (three vertices A, B, C with edges AB, AC, BC; i.e. The Turn graph T(n,r) is an example of an extremal graph.

 

For instance, the question of how many edges an n-vertex graph can have before it must contain as subgraph a clique of size k is answered by Turn’s theorem. Notes[edit]. In the example above, H was the set of n-vertex graphs, P was the property of being cyclic, and u was the number of edges in the graph. Turn also found the (unique) largest graph not containing Kk which is named after him, namely the Turn graph. More abstractly, it studies how global properties of a graph influence local substructures of the graph.[1]. 24365d85ca

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