Prove that r(2K2,K3) = 5.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Prove that r(2K2,K3) = 5.

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Step 1

The objective is to prove that r2K2,K3=5

In a red blue colored K6 let it be K1,5 since all edges are edges are incident with the same vertex the red graph does not contain 2K2

The blue graph graph does not contain 2K2.

The blue graph is K5+K1 which does not contain 8K2.

This shows that r2K2,K3=5.

Now consider a red blue colored K5 that does not contain a red 2K2 or a blue K3.

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