The TCS Ignite Open Lab – Kickoff Challenge - 1The Challenge

Consider the graph G0 with 3 components which are triangles. G0 has 9 vertices labeledA to I and 9 edges (A, B), (B, C) … as shown below.

If each vertex of G0 is assigned a red or a green color, then we say that an edgeis colored if its ends have different colors.

Ajai and Rekha color the vertices of G0 in the following manner. Ajai proposes acolor (red or green) and Rekha chooses the vertex to apply this color. After 9 turns,

all the vertices of G0 are colored and the number of colored edges is counted.Suppose Ajai would like to maximize the number of colored edges while Rekha would

like to minimize the number of colored edges. Assuming optimal play from bothplayers, how many edges will be colored? Explain your reasoning.

Scope and EffortTotal expected effort is about one hour.PrerequisitesAny science graduate registered in Open Ignite can attempt this challenge. Thechallenge only tests your analytical reasoning ability.Submission ProcessYou will need to submit a document containing the solution as well as the steps you havefollowed to arrive at the solution. The submissions can be in txt, .doc or .pdf formatEvaluationYou will be evaluated on the following parameters.S.No. Parameter1. Correctness of solution.2. A detailed explanation of the solution.4