commit dd9f27c6bd922eadbce5d9be4053da5ef61470fd
parent 7c6c154be38ed3b92f24673e92e5be4ddd47dcc0
Author: Antoine Amarilli <a3nm@a3nm.net>
Date: Thu, 23 Apr 2026 17:35:56 +0200
Merge remote-tracking branch 'origin/master'
Diffstat:
2 files changed, 4 insertions(+), 0 deletions(-)
diff --git a/graph_square b/graph_square
@@ -10,6 +10,8 @@ Three variants:
- connecting vertices with a [walk] of length *exactly* two (but potentially also an edge): this is [graph_exact_square]
- connecting vertices with a distance *exactly* two: this is [graph_exact_distance_square]
+The square of the [line_graph], and the [line_graph] of the square, are essentially always [Hamiltonian] for [connected_graphs], cf [nebesky1973line]
+
Up: [graph_exponentiation]
See also: [radoszewski2011hamiltonian], [graph_cube], [graph_square_root], [graph_exact_square]
diff --git a/line_graph b/line_graph
@@ -8,6 +8,8 @@ They can be recognized in [linear_time]
They have a [Hamiltonian_cycle] if the original graph has a [Hamiltonian_cycle]: cf [balakrishnan2012textbook], Corollary 6.5.5 and [harary1965eulerian]
+The [graph_square] of the line graph, and the line graph of the [graph_square], are essentially always [Hamiltonian] for [connected_graphs], cf [nebesky1973line]
+
Up: [graph_basic_notions]
See also: [dual_hypergraph], [dual_graph], [incidence_graph]
