论文信息 - Forbidden induced partial orders

Forbidden induced partial orders

Abstract For each finite partial order P , we consider the size of the set Forb ind n (P) of partial orders on n labelled points containing no induced copy of P . We show that | Forb ind n ( P )| = 2 o ( n 2 ) unless P has height at least 3, in which case | Forb ind n ( P )| = 2 n 2 /4+ o ( n 2 ) . We show that | Forb ind n ( P )| n ! c n for some constant c if and only if P is either an antichain or one of ten small partial orders. Between these extremes, we consider the question of which P have | Forb ind n ( P )| = n O ( n ) .

[1] Peter J. Cameron. On the probability of connectedness , 1997, Discret. Math..

[2] Felix Lazebnik,et al. New Examples of Graphs without Small Cycles and of Large Size , 1993, Eur. J. Comb..

[3] I. Rival. Algorithms and Order , 1988 .

[4] Jacques Tits. Géométries polyédriques et groupes simples , 1963 .

[5] W. Trotter,et al. Combinatorics and Partially Ordered Sets: Dimension Theory , 1992 .

[6] H. Prömel,et al. Excluding Induced Subgraphs III: A General Asymptotic , 1992 .

[7] M. El-Zahar. Enumeration of Ordered Sets , 1989 .

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

[9] G. Brightwell,et al. The number of partial orders of fixed width , 1996 .

[10] Felix Lazebnik,et al. Properties of Certain Families of 2k-Cycle-Free Graphs , 1994, J. Comb. Theory, Ser. B.

[11] V. E. Alekseev. On the entropy values of hereditary classes of graphs , 1993 .

[12] Richard P. Stanley. Enumeration of posets generated by disjoint unions and ordinal sums , 1974 .

[13] Graham R. Brightwell,et al. The Average Number of Linear Extensions of a Partial Order , 1996, J. Comb. Theory, Ser. A.

[14] B. Rothschild,et al. Asymptotic enumeration of partial orders on a finite set , 1975 .

[15] Ronald L. Graham,et al. The Mathematics of Paul Erdős II , 1997 .