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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.)

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.)

Advanced Engineering Mathematics
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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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.)
Transcribed Image Text: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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