Contribution
1-Tough cocomparability graphs are hamiltonian

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Abstract

We show that every 1-tough cocomparability graph has a Hamilton cycle. This settles a conjecture of Chvàtal for the case of cocomparability graphs. Our approach is based on exploiting the close relationship of the problem to the scattering number and the path cover number.

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This research was supported in part by the Office of Naval Research under Grant No. N0014-91-J-1693 and by the Natural Sciences and Engineering Research Council of Canada under Grant No. OGP0001798.