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Results tagged with hamiltonian-graphs
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user 125498
A Hamiltonian graph (directed or undirected) is a graph that contains a Hamiltonian cycle, that is, a cycle that visits every vertex exactly once.
4
votes
Accepted
Does 2-connectivity imply Hamiltoniancy for subgraphs of the rook graph
It's known that $3\leq c \leq7$.
$S$ is the class of line graphs of bipartite graphs, by ISGCI.
The line graph of this graph is 2-connected and non-Hamiltonian, so $c\geq3$.
Siming Zhan proved tha …
- 9,501
5
votes
Accepted
Is every $k$-edge connected $k$-regular graph Hamiltonian?
Assume $k \geq 4$, since, for $k=2$, the answer for both questions is yes, and for $k=3$, no, as there's the Petersen graph.
The answer to the first question is no. To see this, we only need to prove …
- 9,501
2
votes
Accepted
Which are good algorithms for finding Hamiltonian path (not necessarily a circle) up to now?
The Hamiltonian path problem is NP-complete in general, so only heuristics could exist if P≠NP.
The rotation-extension heuristic may be the simplest heuristic:
Input: undirected graph G with size n …
- 9,501