In an m-cycle system C of order n (n greater than or equal to m greater than or equal to 3 integers), the blocks are the vertex sets of n(n - 1)/(2m) cycles C-i of length m such that each edge of the complete graph K-n belongs to precisely one cycle C-i is an element of C. We investigate m-cycle systems which admit vertex partitions into two or more classes in such a way that each class meets every cycle of Ce. Relatively small systems (with n less than or equal to 2(m)/(em)) are always '2-colorable' in this sense; moreover, for every constant c, if n less than or equal to cm, then a partition into c'm/log m classes exists (where the constant c' depends only on c). (C) 1999 Elsevier Science B.V. All rights reserved.
Disjoint blocking sets in cycle systems
MILICI, Salvatore;
1999-01-01
Abstract
In an m-cycle system C of order n (n greater than or equal to m greater than or equal to 3 integers), the blocks are the vertex sets of n(n - 1)/(2m) cycles C-i of length m such that each edge of the complete graph K-n belongs to precisely one cycle C-i is an element of C. We investigate m-cycle systems which admit vertex partitions into two or more classes in such a way that each class meets every cycle of Ce. Relatively small systems (with n less than or equal to 2(m)/(em)) are always '2-colorable' in this sense; moreover, for every constant c, if n less than or equal to cm, then a partition into c'm/log m classes exists (where the constant c' depends only on c). (C) 1999 Elsevier Science B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
