Graph Theory By Narsingh Deo Exercise — Solution

Introduction to Graph Theory

• Rule: A graph is non-planar if and only if it contains a subgraph homeomorphic to $K_5$ (complete graph on 5 vertices) or $K_3,3$ (complete bipartite graph on $3+3$ vertices).

Chapter 5: Trees and Forests

5.1

Detailed breakdown:

• GitHub Repositories: Search for solutions-to-graph-theory-deo. A notable repository by user graph_theory_nerd contains fully written solutions to 60% of the problems in Chapters 2 (Paths & Circuits) and 5 (Planar Graphs). These are peer-reviewed by open-source contributors.
• YouTube Playlists: Channels like "TrevTutor" or "NPTEL Graph Theory" walk through Deo-style problems. While not exact solutions, they teach the methodology to solve the exercise sets.
• AI Assistants (Use Prompt Engineering): You can ask ChatGPT or Claude: “Provide a step-by-step solution to exercise 7.4 from Graph Theory by Narsingh Deo, focusing on vertex coloring lower bounds.” Always cross-check the AI’s logic, as LLMs occasionally hallucinate graph proofs.

• Graphviz (for large graphs)
• GeoGebra (quick sketching)
• Plain paper and colored pens (most effective)