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- Title
Closure and Hamilton-Connected Claw-Free Hourglass-Free Graphs.
- Authors
Ryjáček, Zdeněk; Xiong, Liming; Yin, Jun
- Abstract
The closure $$\mathrm{cl}(G)$$ of a claw-free graph $$G$$ is the graph obtained from $$G$$ by a series of local completions at eligible vertices, as long as this is possible. The construction of an SM-closure of $$G$$ follows the same operations, but if $$G$$ is not Hamilton-connected, then the construction terminates once every local completion at an eligible vertex leads to a Hamilton-connected graph. Although [see e.g. Ryjáček and Vrána (J Graph Theory 66:137-151, )] $$\mathrm{cl}(G)$$ may be Hamilton-connected even if $$G$$ is not, we show that if $$G$$ is a 2-connected claw-free graph with minimum degree at least 3 such that its SM-closure is hourglass-free, then $$G$$ is Hamilton-connected if and only if the closure $$\mathrm{cl}(G)$$ of $$G$$ is Hamilton-connected.
- Subjects
HAMILTONIAN graph theory; HOURGLASSES; GRAPH connectivity; GEOMETRIC vertices; GEOMETRICAL constructions; MATHEMATICAL analysis
- Publication
Graphs & Combinatorics, 2015, Vol 31, Issue 6, p2369
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-014-1490-5