Posets and VPG Graphs

Elad Cohen; Martin Charles Golumbic; William T. Trotter; Ruidong Wang

doi:10.1007/s11083-015-9349-9

Posets and VPG Graphs

Elad Cohen
, Martin Charles Golumbic
, William T. Trotter
, Ruidong Wang

Department of Computer Science

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

Abstract

We investigate the class of intersection graphs of paths on a grid (VPG graphs), and specifically the relationship between the bending number of a cocomparability graph and the poset dimension of its complement. We show that the bending number of a cocomparability graph G is at most the poset dimension of the complement of G minus one. Then, via Ramsey type arguments, we show our upper bound is best possible.

Original language	English
Pages (from-to)	39-49
Number of pages	11
Journal	Order
Volume	33
Issue number	1
DOIs	https://doi.org/10.1007/s11083-015-9349-9
State	Published - 1 Mar 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.

Keywords

Bending number
Cocomparability graph
Dimension
Poset
Product Ramsey theorem

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology
Computational Theory and Mathematics

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10.1007/s11083-015-9349-9

Cite this

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AB - We investigate the class of intersection graphs of paths on a grid (VPG graphs), and specifically the relationship between the bending number of a cocomparability graph and the poset dimension of its complement. We show that the bending number of a cocomparability graph G is at most the poset dimension of the complement of G minus one. Then, via Ramsey type arguments, we show our upper bound is best possible.

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KW - Cocomparability graph

KW - Dimension

KW - Poset

KW - Product Ramsey theorem

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Posets and VPG Graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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