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eulers formula
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Undergraduate
By
Shiva Kintali
on Oct. 3, 2013 | Updated Jan. 4, 2018
Planar graphs and girth
Let \(G\) be an \(n\)-vertex simple connected planar graph with girth \(k\). Prove that \(G\) has at most \((n-2)\cdot \frac{k}{k-2}\) edges. Use this to prove that the Petersen graph is nonplan…
Mathematics
Graph Theory
eulers formula
girth
petersen graph
planar graphs
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Undergraduate
By
Shiva Kintali
on June 29, 2012 | Updated Dec. 6, 2017
Coloring Planar Graphs
Prove that every planar graph has at least one vertex of degree at most five. Conclude that planar graphs are six-colorable. Prove that every triangle-free planar graph has at least one vertex of deg…
Mathematics
Graph Theory
eulers formula
planar graphs
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