Question 8 (20 marks) denote by x(g) the chromatic mumber of a graph g (a) let g be a graph with no 3-cycle. let ei and e2 be two distinct edges of g with a common end-vertex. let h = g - (e1,e2} be the spanning subgraph of g obtained from g by deleting e and e2. prove that x(g)-1x(h) x(g). (b) suppose that g is a graph and v is a cut-vertex of g. prove that there exist subgraphs gi and g2 of g such that g giug2, v(g)n v(g2) = {v} and max{x(gi), x(g2)}. x(g)

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step-by-step explanation:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

b

step-by-step explanation:

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)