Degree conditions and cycle extendability"
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چکیده
A non-Hamiltonian cycle C in a graph G is extendable if there is a cycle C' in G with V(C')= V(C) with one more vertex than C. For any integer k~>0, a cycle C is k-chord extendable if it is extendable to the cycle C' using at most k of the chords of the cycle C. It will be shown that if G is a graph of order n, then 6(G)>3n/4-1 implies that any proper cycle is 0-chord extendable, 6(G)>5n/9 implies that any proper cycle is 1-chord extendable, and 6(G)>Ln/2 j implies that any proper cycle is 2-chord extendable. Also, each of these results is sharp in the sense that the minimum degree condition cannot, in general, be lowered.
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