Hard graph theory problem:

Thread starter voodoomathema
Start date Oct 21, 2009
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Graph Graph theory Hard Theory

In summary, hard graph theory problems involve finding the optimal solution for graphs with a large number of vertices and edges. These problems are considered "hard" due to their complexity and often require advanced techniques and algorithms to solve. They have real-life applications in optimizing transportation and computer networks, as well as solving scheduling problems. Common techniques used to solve these problems include depth-first search, breadth-first search, Dijkstra's algorithm, and dynamic programming. Improving skills in solving these problems involves practice, understanding of algorithms and techniques, studying and analyzing different problems, and seeking help from experts.

Oct 21, 2009

voodoomathema

If G is a connected graph with a cut-vertex v and G1 is a component of G-v, then show that the induced subgraph <V(G1)U{v}> of G need NOT be a block of G.

I guess all I would need is a counterexample, but I can't come up with one.

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Oct 21, 2009

Office_Shredder

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Think of some standard examples of graphs that aren't blocks. Try connecting two of them through a single vertex

Last edited: Oct 21, 2009

1. What is hard graph theory problem?

Hard graph theory problem is a mathematical problem that involves finding the optimal solution to a given graph with a large number of vertices and edges. It is a challenging problem because it requires advanced techniques and algorithms to solve.

2. What makes a graph theory problem "hard"?

A graph theory problem is considered "hard" when it requires complex algorithms and techniques to find the optimal solution. These problems often involve a large number of vertices and edges, making them challenging to solve.

3. What are some real-life applications of hard graph theory problems?

Hard graph theory problems have many real-life applications, such as optimizing transportation networks, designing efficient computer networks, and solving scheduling problems in industries such as manufacturing and logistics.

4. What are some common techniques used to solve hard graph theory problems?

Some commonly used techniques to solve hard graph theory problems include depth-first search, breadth-first search, Dijkstra's algorithm, and dynamic programming. These techniques help in finding the optimal solution by exploring different paths in the graph.

5. How can I improve my skills in solving hard graph theory problems?

Improving skills in solving hard graph theory problems requires practice and understanding of various algorithms and techniques used in graph theory. It is also beneficial to study and analyze different graph theory problems and their solutions to gain a better understanding of the subject. Additionally, participating in competitions and seeking help from experts can also help in improving skills.