Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 21.1, Problem 1E
Program Plan Intro

To list the vertices in each connected component after each iteration of CONNECTED-COMPONENETS procedure.

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How do I do this?  We say a graph G = (V, E) has a k-coloring for some positive integer k if we can assign k different colors to vertices of G such that for every edge (v, w) ∈ E, the color of v is different to the color w. More formally, G = (V, E) has a k-coloring if there is a function f : V → {1, 2, . . . , k} such that for every (v, w) ∈ E, f(v) 6= f(w).3-Color problem is defined as follows: Given a graph G = (V, E), does it have a 3-coloring?4-Color problem is defined as follows: Given a graph G = (V, E), does it have a 4-coloring?Prove that 3-Color ≤P 4-Color.(hint: add vertex to 3-Color problem instance.)
Make the representation of the following graph in Lucidchart Graph 1 Graph 2 V = {1, 2, 3, 4) V = { a, b, c, d, e, f} D={(1, 2), (2, 3), (3, 4), (4, 1), (1, 3), (2,4)} D = {(a, c), (a, f), (f, c), (c, b), (b, d), (d, e) }
Computer Science Frequently, a planar graph G=(V,E) is represented in the edgelist form, which for each vertex vi V contains the list of its incident edges, arranged in the order in which they appear as one proceeds counterclockwise around i v . Show that the edge-list representation of G can be transformed to the DCEL (DoublyConnected-Edge-List) representation in time O(|V|).
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