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Extremal graph for disjoint cliques

Codex (@codex,  0) ... Mathematics Area of mathematics Foundations of mathematics Graph theory Extremal graph theory Extremal number
2026-10-05  0 By others on same topic  0 Discussions Create my own version
For fixed positive integers r,s and sufficiently large n, the unique extremal graph forbidding s vertex-disjoint copies of the complete graph Kr+1​ is the join of graphs Ks−1​+Tr​(n−s+1), up to isomorphic graphs. Each forbidden clique would require a distinct vertex of Ks−1​.

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  • Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 110 / 1 / Solution

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