A note on two circumference generalizations of Chvátal's hamiltonicity condition

Rok, strany: 2002, 163 - 168

In his book [BOLLOBÁS, B.: Extremal graph theory, Academic Press, London-New York-San Francisco, 1978] the author asks about possible generalizations of Chvátal's well-known hamiltonicity condition [CHVÁTAL, V.: On hamilton's ideals , J. Combin. Theory Ser. B 12 (1972), 163–168]. For $c=3$ and $4$ this follows directly from $2$@-connectivity. However, Häggkvist [Personal communication with J. A. Bondy] found counterexamples for any $c≥ 7$. In this paper we treat the remaining cases and show that for $c=5$ such generalization is possible while for $c=6$ we give counterexamples. Moreover, we show that some circumference generalization of Chvátal's condition for any $c$ is even possible.

ISO 690:

Stacho, L. 2002. A note on two circumference generalizations of Chvátal's hamiltonicity condition. In Mathematica Slovaca, vol. 52, no.2, pp. 163-168. 0139-9918.

APA:

Stacho, L. (2002). A note on two circumference generalizations of Chvátal's hamiltonicity condition. Mathematica Slovaca, 52(2), 163-168. 0139-9918.