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Undergraduate
By
diego
on June 8, 2012 | Updated Dec. 6, 2017
The cube of a connected graph is hamiltonian
Prove that the vertices of any connected graph \(G\) can be listed in a cyclic order so that the distance in \(G\) of every two consecutive vertices is at most \(3\). Moreover, show that this can be …
Computer Science
Mathematics
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Graph Theory
hamiltonian cycle
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Undergraduate
By
Shiva Kintali
on June 5, 2012 | Updated Dec. 6, 2017
Properties of Petersen Graph
Petersen Graph is the graph shown below : Prove the following properties of the Petersen Graph : It is not planar. It is strongly-regular. It has a Hamiltonian path but no Hamiltonian Cycle. It i…
Mathematics
Graph Theory
connectivity
hamiltonian cycle
matching
petersen graph
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Graduate
By
Shiva Kintali
on June 12, 2012 | Updated Dec. 6, 2017
Hamiltonian cycles in odd graphs
Let \(G\) be a graph such that all vertices of \(G\) have odd degree. Let \(e\) be any edge of \(G\). Prove that there are an even number of Hamiltonian cycles using \(e\).
Mathematics
Graph Theory
hamiltonian cycle
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Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Hamiltonicity of Line Graphs
Let \(G=(V,E)\) be a simple undirected graph. The line graph \(L(G)\) of \(G\) is defined as follows: Each vertex in \(L(G)\) corresponds to an edge in \(G\), and two vertices are connected by an e…
Mathematics
Graph Theory
hamiltonian cycle
line graph
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Undergraduate
By
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Basics of Hamiltonicity
Let \(G(V,E)\) be a simple graph with \(n\) vertices and minimum degree \(\delta\). Also, for every two vertices \(x, y \in V\), \(|N(x) \cup N(y)| + \delta \ge n + 10\). Prove that \(G\) has a Hami…
Mathematics
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hamiltonian cycle
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