The Non-Crossing Graph

Two sets are non-crossing if they are disjoint or one contains the other. The noncrossing graph NCn is the graph whose vertex set is the set of nonempty subsets of [n] = {1, . . . , n} with an edge between any two non-crossing sets. Various facts, some new and some already known, concerning the chromatic number, fractional chromatic number, independence number, clique number and clique cover number of this graph are presented. For the chromatic number of this graph we show: n(loge n - (1)) (NCn) n( log2 n - 1).

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Nathan Linial, Michael E. Saks, David Statter
• Keywords: Chromatic Number, COMBINATORICS 2006, Fractional Chromatic Number, Noncrossing Graph Ncn