3. The number of maximal cliques in a graph must obviously be an integer, so when the Moon-Moser bound 3"/3 is not an integer, we can strengthen it by rounding it down to an integer: every graph with n vertices has at most [3"/3] maximal cliques. |(a) Find a graph on four vertices with exactly this many maximal cliques. (b) Find a graph on five vertices with exactly this many maximal cliques. (c) (265 students only) A more precise bound, valid for all n, is that the number of maximal cliques is 2" 3b where a e {0, 1, 2} and 3b+ 2a = n. Find the smallest n for which this bound differs from [3"/3]. Solution to problem 3 goes here.

3. The number of maximal cliques in a graph must obviously be an integer, so when the Moon-Moser bound 3"/3 is not an integer, we can strengthen it by rounding it down to an integer: every graph with n vertices has at most [3"/3] maximal cliques. |(a) Find a graph on four vertices with exactly this many maximal cliques. (b) Find a graph on five vertices with exactly this many maximal cliques. (c) (265 students only) A more precise bound, valid for all n, is that the number of maximal cliques is 2" 3b where a e {0, 1, 2} and 3b+ 2a = n. Find the smallest n for which this bound differs from [3"/3]. Solution to problem 3 goes here.

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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36. Let G be a simple graph on n vertices and has k components. Then the number m of edges of G satisfies n-k ≤m if G is a null graph. This statement is A. sometimes true B. always true C. never true D. Neither true nor false
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