Graph Theory Problems
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Graph Theory Problems
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Graph Theory Eulerian Path Hamiltonian Path Four Color Theorem Graph Coloring and Chromatic Numbers Hall s Marriage Theorem Applications of Hall s Marriage Theorem Art Gallery Problem Wiki Collaboration Graph Combinatorial Optimization Group actions If the chromatic number is 6, then the graph is not planar; the 4-color theorem states that all planar graphs can be colored with 4 or fewer colors. 3 Find the chromatic number of each of the following graphs.
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Graph Theory ProblemsProblem 1 – There are 25 telephones in Geeksland. Is it possible to connect them with wires so that each telephone is connected with exactly 7 others. Solution – Let us suppose that such an arrangement is possible. This can be viewed as a graph in which telephones are represented using vertices and wires using the edges. The edges e1 e2 en 1 form a spanning tree for G Prove that this spanning tree has minimum cost Exercise 5 E 6 2 Prove that if the edge costs of G are distinct there is exactly one minimum cost spanning tree Give an example of a graph G with more than one minimum cost spanning tree
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