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JEST 2019 Descriptive Q1 (8 Marks)

dan31 asked in Graph Theory Feb 17, 2019 edited Feb 17, 2019 by dan31

405 views

1 vote

1 vote

Suppose that G contains a cycle C, and a path of length at least k between some two
vertices of C. Show that G contains a cycle of length at least √k.

jest
2019
discrete-mathematics

dan31 asked in Graph Theory Feb 17, 2019 edited Feb 17, 2019 by dan31

by dan31

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1 comment

commented Feb 18, 2019

Couldn't solve this in the exam 😶 Looked up online and found this : https://math.stackexchange.com/questions/1541302/show-that-g-contains-a-cycle-of-length-at-least-sqrt-k

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dan31 asked in Graph Theory Feb 17, 2019

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JEST 2019 Descriptive Q2 (8 Marks)
Given a sequence $a_1$, $a_2$ , $a_3$ ... $a_n$ of any different positive integers, exhibit an arrangement of integers between 1 and $n^2$ which has no increasing or decreasing subsequence of length n+1.

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dan31 asked in Algorithms Feb 17, 2019

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JEST 2019 Descriptive Q4 (8 Marks)
Give an efficient algorithm for maximum size rectangle binary sub-matrix with all 1s . [Complexity should be O($n^c$)] (Memory based – Original question had a lot of added details)

dan31 asked in Algorithms Feb 17, 2019

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vivek_mishra asked in Set Theory & Algebra Feb 17, 2019

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JEST 2019
Let ${(0,1)}^n$ set of all binary string of length n. Hamming sphere of radius around a string C in ${(0,1)}^n$ is the set of all strings d$\epsilon$ ${(0,1)}^n$ that differ from C in at most r of n position, S(C,r) for n=2k+1 For C,C’ $\epsilon$ ${(0,1)}^n$ S(C,k) and S(C’,k) are disjoint couldn't remember rest of the options.

vivek_mishra asked in Set Theory & Algebra Feb 17, 2019

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jest
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dan31 asked in Set Theory & Algebra Feb 17, 2019

585 views

JEST 2019 Descriptive Q3 (8 Marks)
Determine the number of functions f:{1,2,3…,n}→{1995,1996} satisfying the condition that f(1)+f(2)+…f(n) is odd.

dan31 asked in Set Theory & Algebra Feb 17, 2019

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jest2019
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