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Results tagged with hamiltonian-graphs
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user 171032
A Hamiltonian graph (directed or undirected) is a graph that contains a Hamiltonian cycle, that is, a cycle that visits every vertex exactly once.
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Is there a monograph or review of Hamiltonian cycles of graphs (or long cycles of graphs)？
In graph theory, a Hamiltonian cycle is a cycle that visits each vertex exactly once. Hamiltonian cycle has a long history, and I have followed some articles.
We can find plenty of examples of Hamil …
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Has there been progress on Hamiltonicity in 4-connected claw-free graphs with a constant max...
In 1984, Matthews and Sumner [1] conjectured that every 4-connected claw-free graph is Hamiltonian, and this conjecture is still wide open.
I would like to know if there has been any progress on this …
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Are there 4-connected planar non-hamilton multi-graphs?
Tutte proved the famous result: Every planar 4-connected graph has a hamiltonian cycle. But I read in Section 111.6.5 on book Eulerian Graphs and Related Topics that the author Herbert Fleischner pl …
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Number of Hamiltonian cycles on 24-cell graph
We can run the code from github due to Jorik Jooken. The folder contains an algorithm ("countHamiltonianCyclesHeldKarp") for counting the number of Hamiltonian cycles (based on the Held-Karp algorith …
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How many 20-vertex 2-connected 5-regular non-Hamiltonian graphs are there?
As for the question in title, I attempted to use nauty to obtain them, but it has been running on my computer for nearly three days without producing any results.
./geng 20 -C -d5 -D5 | ./hamheurist …
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The perfect matching problem of planar graph
We know that connectivity is closely related to the Hamiltonian of planar graphs.
The most famous result is the Tutte theorem.
Theorem (Tutte, 1956). A 4-connected planar graph has a Hamiltonian cycl …
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The perfect matching problem of planar graph
The following article provides a positive answer to my question. Yes, it is possible to prove that a 4-connected planar graph has a perfect matching or almost perfect matching even without using the H …
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is a 4-connected planar graph still Hamiltonian after removing an edge?
We know that 4-connected planar graphs are Hamiltonian(by the known Tutte Theorem). Additionally, Thomas and Yu [1] proved that removing two vertices from a 4-connected planar graph still preserves H …
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