Polytopality of maniplexes

Jorge Garza-Vargas; Isabel Hubard

doi:10.1016/j.disc.2018.02.017

Polytopality of maniplexes

Jorge Garza-Vargas
, Isabel Hubard

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

17 Scopus citations

Abstract

Given an abstract polytope P, its flag graph is the edge-coloured graph whose vertices are the flags of P and whose i-edges correspond to i-adjacent flags. Flag graphs of polytopes are maniplexes. On the other hand, a maniplex need not be the flag graph of a polytope. It is natural to ask when does a maniplex is the flag graph of a polytope. In this paper we give necessary and sufficient conditions (in terms of graphs) on a maniplex to be (isomorphic to) the flag graph of a polytope. For this, given a maniplex M, we define a poset P_M and determine when is P_M an abstract polytope. Moreover, in such case, we show that M is isomorphic to the flag graph of P_M.

Original language	English (US)
Pages (from-to)	2068-2079
Number of pages	12
Journal	Discrete Mathematics
Volume	341
Issue number	7
DOIs	https://doi.org/10.1016/j.disc.2018.02.017
State	Published - Jul 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Keywords

Abstract polytopes
Edge-coloured graphs
Maniplexes
Polytopal maps

Access to Document

10.1016/j.disc.2018.02.017

Cite this

@article{dea2114eade6410282b47c5c365e1c98,

title = "Polytopality of maniplexes",

abstract = "Given an abstract polytope P, its flag graph is the edge-coloured graph whose vertices are the flags of P and whose i-edges correspond to i-adjacent flags. Flag graphs of polytopes are maniplexes. On the other hand, a maniplex need not be the flag graph of a polytope. It is natural to ask when does a maniplex is the flag graph of a polytope. In this paper we give necessary and sufficient conditions (in terms of graphs) on a maniplex to be (isomorphic to) the flag graph of a polytope. For this, given a maniplex M, we define a poset PM and determine when is PM an abstract polytope. Moreover, in such case, we show that M is isomorphic to the flag graph of PM.",

keywords = "Abstract polytopes, Edge-coloured graphs, Maniplexes, Polytopal maps",

author = "Jorge Garza-Vargas and Isabel Hubard",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

month = jul,

doi = "10.1016/j.disc.2018.02.017",

language = "English (US)",

volume = "341",

pages = "2068--2079",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier B.V.",

number = "7",

}

TY - JOUR

T1 - Polytopality of maniplexes

AU - Garza-Vargas, Jorge

AU - Hubard, Isabel

PY - 2018/7

Y1 - 2018/7

N2 - Given an abstract polytope P, its flag graph is the edge-coloured graph whose vertices are the flags of P and whose i-edges correspond to i-adjacent flags. Flag graphs of polytopes are maniplexes. On the other hand, a maniplex need not be the flag graph of a polytope. It is natural to ask when does a maniplex is the flag graph of a polytope. In this paper we give necessary and sufficient conditions (in terms of graphs) on a maniplex to be (isomorphic to) the flag graph of a polytope. For this, given a maniplex M, we define a poset PM and determine when is PM an abstract polytope. Moreover, in such case, we show that M is isomorphic to the flag graph of PM.

AB - Given an abstract polytope P, its flag graph is the edge-coloured graph whose vertices are the flags of P and whose i-edges correspond to i-adjacent flags. Flag graphs of polytopes are maniplexes. On the other hand, a maniplex need not be the flag graph of a polytope. It is natural to ask when does a maniplex is the flag graph of a polytope. In this paper we give necessary and sufficient conditions (in terms of graphs) on a maniplex to be (isomorphic to) the flag graph of a polytope. For this, given a maniplex M, we define a poset PM and determine when is PM an abstract polytope. Moreover, in such case, we show that M is isomorphic to the flag graph of PM.

KW - Abstract polytopes

KW - Edge-coloured graphs

KW - Maniplexes

KW - Polytopal maps

UR - https://www.scopus.com/pages/publications/85046749547

UR - https://www.scopus.com/pages/publications/85046749547#tab=citedBy

U2 - 10.1016/j.disc.2018.02.017

DO - 10.1016/j.disc.2018.02.017

M3 - Article

AN - SCOPUS:85046749547

SN - 0012-365X

VL - 341

SP - 2068

EP - 2079

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 7

ER -

Polytopality of maniplexes

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this