Consider a directed graph G = (V, E), and two distinct vertices u, v E V. Recall that a set of U-V paths is non-overlapping if they have no edges in common among them, and a set C of edges disconnects from u if in the graph (V, E-C) there is no path from u to v. Suppose we want to show that for any set of non-overlapping paths P and any disconnecting set C, |P| ≤ |C|. Consider the proof that defines A = P, B = C and f(path q) = qn C, and applies the Pigeonhole Principle to obtain the result. True or False: f is a well-defined function (i.e. it satisfies the 3 properties of a well- defined function). True False

Consider a directed graph G = (V, E), and two distinct vertices u, v E V. Recall that a set of U-V paths is non-overlapping if they have no edges in common among them, and a set C of edges disconnects from u if in the graph (V, E-C) there is no path from u to v. Suppose we want to show that for any set of non-overlapping paths P and any disconnecting set C, |P| ≤ |C|. Consider the proof that defines A = P, B = C and f(path q) = qn C, and applies the Pigeonhole Principle to obtain the result. True or False: f is a well-defined function (i.e. it satisfies the 3 properties of a well- defined function). True False

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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