1. Raj wants to paint a checkered pathway in a park (really really big) with red and green paints. He wants to paint all the squares on the pathway such that it has no rectangle with all the corners in the same color (Let us call them the mono-corner rectangles). The picture on the left shows a correct case and picture on the right shows a failure case i.e. a mono- corner rectangle (since all 4 corners of the rectangle have same color). (a) Prove that it is impossible for Raj to paint all the squares of the pathway without any mono-corner rectangles. (b) Prove that using 3 colors instead of 2 will not help avoid the mono- corner rectangles.

1. Raj wants to paint a checkered pathway in a park (really really big) with red and green paints. He wants to paint all the squares on the pathway such that it has no rectangle with all the corners in the same color (Let us call them the mono-corner rectangles). The picture on the left shows a correct case and picture on the right shows a failure case i.e. a mono- corner rectangle (since all 4 corners of the rectangle have same color). (a) Prove that it is impossible for Raj to paint all the squares of the pathway without any mono-corner rectangles. (b) Prove that using 3 colors instead of 2 will not help avoid the mono- corner rectangles.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Needed urgently... do it fast as possible... do both parts (a) and (b)

1. Raj wants to paint a checkered pathway in a park (really really big) with
red and green paints. He wants to paint all the squares on the pathway
such that it has no rectangle with all the corners in the same color (Let
us call them the mono-corner rectangles). The picture on the left shows
a correct case and picture on the right shows a failure case i.e. a mono-
corner rectangle (since all 4 corners of the rectangle have same color).
(a) Prove that it is impossible for Raj to paint all the squares of the
pathway without any mono-corner rectangles.
(b) Prove that using 3 colors instead of 2 will not help avoid the mono-
corner rectangles.

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