Edges in a graph with no triangles

Discrete Mathematics Level 5

A simple graph \(G\) has 200000 edges and for any 3 vertices \(v,w,x,\) at least one of the edges \(vw, wx, xv\) is not present in \(G.\) What is the least number of vertices that \(G\) can have?

Details and assumptions

A simple graph does not have multiple edges between vertices, or self loops.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.