Prove that every graph G with n vertices and chromatic number k = x(G) has at most · (n² – )|edges.(Hint: What is the maximum number of edges possible? How many edges must be missing?)(Hint: You can use as an axiom thatE=1n, where E=1n; = n is minimized when each n¡ = n/k.)

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Answered: Prove that every graph G with n…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find the family of graphs G of order p such that c(G) = p - 2.

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Prove that every graph G with n vertices and chromatic number k = x(G) has at most · (n2 – ) edges. (Hint: What is the maximum number of edges possible? How many edges must be missing?) (Hint: You can use as an axiom that =1 n%, where i=1 n¡ = n is minimized when each n; = n/k.)