The non-crossing graph

Nathan Linial; Michael Saks; David Statter

doi:10.37236/1140

The non-crossing graph

Nathan Linial^*, Michael Saks, David Statter

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	Electronic Journal of Combinatorics
Volume	13
Issue number	1 N
DOIs	https://doi.org/10.37236/1140
State	Published - 25 Jan 2006

Access to Document

10.37236/1140

Cite this

@article{4ba8c21dc82e4acebd52f28f9ccebe7d,

title = "The non-crossing graph",

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).",

author = "Nathan Linial and Michael Saks and David Statter",

year = "2006",

month = jan,

day = "25",

doi = "10.37236/1140",

language = "אנגלית",

volume = "13",

pages = "1--8",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Electronic Journal of Combinatorics",

number = "1 N",

}

TY - JOUR

T1 - The non-crossing graph

AU - Linial, Nathan

AU - Saks, Michael

AU - Statter, David

PY - 2006/1/25

Y1 - 2006/1/25

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=31544461502&partnerID=8YFLogxK

U2 - 10.37236/1140

DO - 10.37236/1140

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:31544461502

SN - 1077-8926

VL - 13

SP - 1

EP - 8

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 1 N

ER -

The non-crossing graph

Abstract

Access to Document

Other files and links

Fingerprint

Cite this