2
votes
Hamiltonian path in bike-lock graph with $1$ known digit
Partial answer to the cycle version.
Case $k=2$, any $n$: The graph has no Hamiltonian cycle. If $n \ge 3$, the graph consists of two $n$-cycles that intersect at a single point $(0,0)$. If $n=2$, the ...
1
vote
Accepted
A property of directed acyclic graph
Preliminary definition. Let $\mathcal{S}$, $\mathcal{S}'$ be two complementary nonempty sets of indices, i.e., $\mathcal{S}\cup \mathcal{S}'=\left\{1,2,\ldots,p\right\}$ and $\mathcal{S}\cap \mathcal{...
Only top scored, non community-wiki answers of a minimum length are eligible
Related Tags
graph-theory × 4638co.combinatorics × 1958
graph-colorings × 476
reference-request × 398
algorithms × 313
pr.probability × 257
spectral-graph-theory × 232
computational-complexity × 184
gr.group-theory × 180
random-graphs × 180
linear-algebra × 162
extremal-graph-theory × 155
discrete-geometry × 154
mg.metric-geometry × 120
matching-theory × 116
combinatorial-optimization × 102
set-theory × 97
trees × 91
perfect-matchings × 90
matrices × 88
infinite-combinatorics × 88
algebraic-graph-theory × 84
bipartite-graphs × 82
hypergraph × 81
directed-graphs × 74