8. (a) A graph has six vertices, every two of which are joined by an edge. Each edge is colored red or white. Show that the graph contains a monochromatic tri- angle (a triangle all of whose vertices have the same color.) (b) Is the result of (a) true for a graph with five vertices? Explain.
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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Figure 9.13 More c
more than once. The numbers of hands shaken by the
other seven people (excluding you) are all different. How
many hands did you shake? How many hands did your
partner shake? Use a graph to aid your solution.
8. (a) A graph has six vertices, every two of which are
joined by an edge. Each edge is colored red or white.
Show that the graph contains a monochromatic tri-
angle (a triangle all of whose vertices have the same
color.)
(b) Is the result of (a) true for a graph with five vertices?
Explain.
9. [BB] A graph has six vertices, every two of which are
joined by an edge. Each vertex is colored red or white.
Show that the graph contains at least two monochromatic
triangles.
10. A graph has six vertices, every two of which are joined
by an edge. Each edge is colored red or white. Show that
the graph contains at least two monochromatic triangles.
11. A cat and a mouse are at the positions indicated in a maze
depicted by the graph of Fig. 9.14.
9.2 Definitions and Basic Prope](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22c3f8b2-10be-45e6-b1e5-3ab272cb7721%2Ffb89003e-f868-4e42-8eb2-45d35bbc5eb9%2Flvx0bzt_processed.jpeg&w=3840&q=75)
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