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- W2030151166 abstract "We prove that a k-connected graph (k⩾2) is Hamiltonian if it is not contractible to one of a specified collection of graphs of order 2k+1. The theorem generalizes a previous result of the authors. The proof partly parallels that of the following, less general, result of Chvátal and Erdös: A k-connected graph containing no independent set of more than k points (k⩾2) is Hamiltonian (∗). Also stated in terms of contractibility are sufficient conditions for graphs to be traceable, Hamiltonian connected or 1-Hamiltonian, respectively. Conditions analogous to (∗) guaranteeing the same properties were found by Chvátal and Erdös and by Lesniak. For traceable and 1-Hamiltonian graphs the contraction theorems sharpen the corresponding analogues of (∗), while equivalence is conjectured for Hamiltonian connected graphs." @default.
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- W2030151166 date "1981-01-01" @default.
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- W2030151166 title "Contraction theorems in Hamiltonian graph theory" @default.
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- W2030151166 doi "https://doi.org/10.1016/0012-365x(81)90022-4" @default.
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