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Results tagged with hamiltonian-graphs
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user 12481
A Hamiltonian graph (directed or undirected) is a graph that contains a Hamiltonian cycle, that is, a cycle that visits every vertex exactly once.
2
votes
Hamiltonian paths in bipartite graphs with 2 sets of "almost" same cardinality
No. Degree $2$ vertex and its neighbors must be on the hamiltonian path in fixed order and there can be many degree $2$ vertices.
- 25.4k
5
votes
Hamiltonicity criteria for sparse graphs
Partial answer.
According to Eppstein
It is known that it is NP-complete to test whether a Hamiltonian cycle exists in a 3-regular graph, even if it is planar (Garey, Johnson, and Tarjan, SIAM J. …
- 25.4k
2
votes
Accepted
Regular graphs with $a$ and $b$ Hamiltonian edges
There are infinite families of $4$ and $5$ regular graphs
with $\rho(G)=1$ using a gadget.
A gadget is graph $GA$ with $2$ vertices $u,v$ of degree $d-1$
and the rest are of degree $d$. The gadget co …
- 25.4k
4
votes
Graphs with many edges avoided by Hamiltonian cycles
The computer found counterexamples to $\rho(G)<1$.
Despite verification, I am not sure this is correct.
$G_1$ on $7$ vertices, $G_2$ on $11$ vertices.
$\rho(G_1)=1,\rho(G_2)=2$
$G_1$:
edges=[(0, 3 …
- 25.4k
5
votes
Efficient Hamiltonian cycle algorithms for graph classes
I am not sure your reduction to Euler cycle is complete.
According to Wikipedia
If a graph G has an Euler cycle, that is, if G is connected and has an even number of edges at each vertex, then the li …
- 25.4k