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Results tagged with hamiltonian-graphs
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user 43266
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
Counterexample. Draw a 4-cycle with vertices A, B, C, D and edges AB, BC, CD, DA; draw another 4-cycle with vertices E, F, G, H and edges EF, FG, GH, HE; draw a third 4-cycle with vertices I, J, K, L …
- 13.4k
6
votes
"Gray code" for building teams
Theorem. The graph $G(n,k)$ is Hamiltonian if $n\ge3$ and $0\lt k\lt n$.
Proof. If $k=1$ or $k=n-1$ it's obvious, because $G(n,k)\cong K_n$ in those cases. Now consider the graph $G=G(n,k)$ where $2\l …
- 13.4k