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Theorem which became a problem.

Source: Iranian Third Round 2020 Combinatorics exam Problem1

November 18, 2020
graph theorycombinatoricsindependent sets

Problem Statement

1)1). Prove a graph with 2n2n vertices and n+2n+2 edges has an independent set of size nn (there are nn vertices such that no two of them are adjacent ). 2)2).Find the number of graphs with 2n2n vertices and n+3n+3 edges , such that among any nn vertices there is an edge connecting two of them
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