Implement Ore's theorem check for Hamiltonian graphs in GenericGraph class #41343
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dcoudert
reviewed
Jan 4, 2026
| if (not self.is_directed() and not self.has_loops() and not self.has_multiple_edges() and n >= 3): | ||
| vertices = list(self) | ||
| ore_holds = True | ||
| for i, u in enumerate(vertices): |
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here you could use from itertools import combinations and then for u, v in combinations(vertices, 2) to list all pairs.
from itertools import combinations
degree = self.degree(labels=True)
ore_holds = all(degree[u] + degree[v] >= n
for u, v in combinations(vertices, 2)
if not self.has_edge(u, v))| # Return a trivial Hamiltonian cycle if possible, else True | ||
| # (Here, we just shortcut and return True, or could construct a cycle) | ||
| from sage.graphs.graph import Graph | ||
| cycle_edges = [(vertices[i], vertices[(i+1)%n]) for i in range(n)] |
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Here you can not ensure that all edges in this list are edges of the graph.
You could implement Palmer's algorithm (see https://en.wikipedia.org/wiki/Ore%27s_theorem) to get a valid cycle.
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Documentation preview for this PR (built with commit 48859cf; changes) is ready! 🎉 |
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📝 Checklist
⌛ Dependencies