This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 1

2013 Princeton University Math Competition, 3
Tags: inequalities , i lost the game
A graph consists of a set of vertices, some of which are connected by (undirected) edges. A [i]star[/i] of a graph is a set of edges with a common endpoint. A [i]matching[/i] of a graph is a set of edges such that no two have a common endpoint. Show that if the number of edges of a graph $G$ is larger than $2(k-1)^2$, then $G$ contains a matching of size $k$ or a star of size $k$.