Hajnal, Andras and Juhász, Istvan and Soukup, Lajos and Szentmiklossy, Zoltan (2010) *Conflict free colorings of (strongly) almost disjoint set-systems.* (Submitted)

| PDF 359Kb |

## Abstract

is called a conflict free coloring of the set-system (with colors) if . The conflict free chromatic number of is the smallest for which admits a conflict free coloring with colors. is a -system if , for all , and is -almost disjoint, i.e. for distinct .

Our aim here is to study for , actually restricting ourselves to and . For instance, we prove that

for any limit cardinal (or ) and integers , GCH implies if , if ;

if then implies and implies ;

GCH implies for ,

V=L implies for ;

the existence of a supercompact cardinal implies the consistency of GCH plus and for ;

CH implies , while implies .

Item Type: | Research Paper |
---|---|

Keywords and phrases: | coloring, conflict-free coloring, almost disjoint, essentially disjoint |

Subjects: | 03E35 Consistency and independence results |

Divisions: | Research Divisions > Set theory and general topology |

Last Modified: | 02 Apr 2010 11:16 |

Repository Staff Only: item control page