The non-crossing graph

Nathan Linial*, Michael Saks, David Statter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Two sets are non-crossing if they are disjoint or one contains the other. The non-crossing 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(logen - Θ(1)) ≤ χ(NCn) ≤ n(⌈log2n⌉ - 1).

Original languageAmerican English
Pages (from-to)1-8
Number of pages8
JournalElectronic Journal of Combinatorics
Volume13
Issue number1 N
DOIs
StatePublished - 25 Jan 2006

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