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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 24E
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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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