论文信息 - Comparability invariance of the fixed point property

Comparability invariance of the fixed point property

We show that the fixed point property is comparability invariant for finite ordered sets; that is, if P and Q are finite ordered sets with isomorphic comparability graphs, then P has the fixed point property if and only if Q does. In the process we give a characterization of comparability invariants which can also be used to give shorter proofs of some known results.

Peter Winkler | W. Poguntke | B. Dreesen

[1] Richard P. Stanley,et al. Two poset polytopes , 1986, Discret. Comput. Geom..

[2] Rainer Schrader,et al. A combinatorial bijection between linear extensions of equivalent orders , 1986, Discret. Math..

[3] M. Golumbic. Algorithmic graph theory and perfect graphs , 1980 .

[4] R. Gysin. Dimension transitiv orientierbarer graphen , 1977 .

[5] William T. Trotter,et al. The dimension of a comparability graph , 1976 .

[6] T. Gallai. Transitiv orientierbare Graphen , 1967 .

[7] Ivan Rival. The Problem of Fixed Points in Ordered Sets , 1980 .

[8] J. C. Arditti,et al. The Dimension of Finite and Infinite Comparability Graphs , 1980 .

[9] Kenneth Baclawski,et al. Fixed points in partially ordered sets , 1979 .