The following questions are mostly on the topic of graph complements.(a) Let G be a graph with ∆(G) ≥ r, where r is a positive integer. Show that either Gcontains a triangle or ̄G contains a Kr.(b) Let G be a graph of order n which contains no triangles.(i) Assume that n = 9. Show that ̄G contains a K4.(ii) Assume that n = 8. Must ̄G contain a K4 ? Justify your answer.
The following questions are mostly on the topic of graph complements.(a) Let G be a graph with ∆(G) ≥ r, where r is a positive integer. Show that either Gcontains a triangle or ̄G contains a Kr.(b) Let G be a graph of order n which contains no triangles.(i) Assume that n = 9. Show that ̄G contains a K4.(ii) Assume that n = 8. Must ̄G contain a K4 ? Justify your answer.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 13E
Related questions
Question
The following questions are mostly on the topic of graph complements.
(a) Let G be a graph with ∆(G) ≥ r, where r is a positive integer. Show that either G
contains a triangle or ̄G contains a Kr.
(b) Let G be a graph of order n which contains no triangles.
(i) Assume that n = 9. Show that ̄G contains a K4.
(ii) Assume that n = 8. Must ̄G contain a K4 ? Justify your answer.
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