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Improved Sufficient Conditions for Hamiltonian Properties

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Bode J.-P., Fricke A., Kemnitz A.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 2

329-334

In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+ 1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.

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1 Discussiones Mathematicae Graph Theory

1 Bode J.-P.

1 Fricke A.

1 Kemnitz A.

1 2015

Wyniki wyszukiwania

Improved Sufficient Conditions for Hamiltonian Properties