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In addition to the general packing problem, we consider packings of graphs in special families where less sparseness is needed.

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Their policies may differ from this site. Kostochka and V. Glebov, A. Kostochka, and V. Kostochka and K. Kostochka, R. Skrekovski, M. Stiebitz, and D. Alon, G.

Extremal problems in combinatorial geometry and Ramsey theory

Brightwell, H. Kierstead, A. Kostochka, and P. Kostochka and G. Gould, A. Kostochka, and G. Some features of this site may not work without it.

Theory of extremal problems

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Introduction to extremal set theory 1. Sperner's theorem

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Discrete mathematics with applications notes

For example, a simple extremal graph theory question is "which acyclic graphs on n vertices have the maximum number of edges? 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. Several foundational results in extremal graph theory are questions of the above-mentioned form. It answers the following question. The complete bipartite graph where the partite sets differ in their size by at most 1, is the only extremal graph with this property. It contains. Similar questions have been studied with various other subgraphs H instead of K 3 ; for instance, the Zarankiewicz problem concerns the largest graph that does not contain a fixed complete bipartite graph as a subgraph, and the even circuit theorem concerns the largest graph without a fixed-length even cycle.

This graph is the complete join of "k-1" independent sets as equi-sized as possible and has at most.