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- W2000467025 abstract "A unified approach to a variety of graph-theoretic problems is introduced. The k-closure Ck(G) of a simple graph G of order n is the graph obtained from G by recursively joining pairs of nonadjacent vertices with degree-sum at least k. It is shown that, for many properties P, one can find a suitable value of k (depending on P and n) such that if Ck(G) has P, then so does G. For instance, if P is the hamiltonian property, one may take k = n. Thus if Cn(G) is hamiltonian, then so is G; in particular, if n ⩾ 3 and Cn(G) is complete, then G is hamiltonian. This condition for a graph to be hamiltonian is shown to imply the well-known conditions of Chvátal and Las Vergnas. The same method, applied to other properties, yields many new theorems of a similar nature." @default.
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- W2000467025 date "1976-01-01" @default.
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- W2000467025 title "A method in graph theory" @default.
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- W2000467025 doi "https://doi.org/10.1016/0012-365x(76)90078-9" @default.
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