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throwing out any vertex there is a n-clique prove that there is a n+1-clique

Source: 239 2001 J8

May 20, 2020
graph theorycombinatorics

Problem Statement

In a graph with 2nāˆ’12n-1 vertices throwing out any vertex the remaining graph has a complete subgraph with nn vertices. Prove that the initial graph has a complete subgraph with n+1n+1 vertices.