The poset of graphs ordered by induced containment

Jason P. Smith (Corresponding Author)

Research output: Contribution to journalArticle

1 Downloads (Pure)

Abstract

We study the poset of all unlabelled graphs with if H occurs as an induced subgraph in G. We present some general results on the Möbius function of intervals of and some results for specific classes of graphs. This includes a case where the Möbius function is given by the Catalan numbers, which we prove using discrete Morse theory, and another case where it equals the Fibonacci numbers, therefore showing that the Möbius function is unbounded. A classification of the disconnected intervals of is presented, which gives a large class of non-shellable intervals. We also present several conjectures on the structure of .
Original languageEnglish
Pages (from-to)348-373
Number of pages26
JournalJournal of Combinatorial Theory, Series A
Volume168
Early online date4 Jul 2019
DOIs
Publication statusPublished - Nov 2019

Fingerprint

Poset
Interval
Graph in graph theory
Discrete Morse Theory
Catalan number
Lame number
Induced Subgraph
Class

Keywords

  • Graph containment
  • Posets
  • Möbius function
  • MOBIUS FUNCTION
  • Mobius function

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

The poset of graphs ordered by induced containment. / Smith, Jason P. (Corresponding Author).

In: Journal of Combinatorial Theory, Series A, Vol. 168, 11.2019, p. 348-373.

Research output: Contribution to journalArticle

@article{85be492f1a9345cf93cb00b848cfd54b,
title = "The poset of graphs ordered by induced containment",
abstract = "We study the poset of all unlabelled graphs with if H occurs as an induced subgraph in G. We present some general results on the M{\"o}bius function of intervals of and some results for specific classes of graphs. This includes a case where the M{\"o}bius function is given by the Catalan numbers, which we prove using discrete Morse theory, and another case where it equals the Fibonacci numbers, therefore showing that the M{\"o}bius function is unbounded. A classification of the disconnected intervals of is presented, which gives a large class of non-shellable intervals. We also present several conjectures on the structure of .",
keywords = "Graph containment, Posets, M{\"o}bius function, MOBIUS FUNCTION, Mobius function",
author = "Smith, {Jason P.}",
note = "I would like to express my gratitude to the anonymous referees for their extremely useful comments and corrections which greatly improved the paper.",
year = "2019",
month = "11",
doi = "10.1016/j.jcta.2019.06.009",
language = "English",
volume = "168",
pages = "348--373",
journal = "Journal of Combinatorial Theory, Series A",
issn = "0097-3165",
publisher = "Elsevier",

}

TY - JOUR

T1 - The poset of graphs ordered by induced containment

AU - Smith, Jason P.

N1 - I would like to express my gratitude to the anonymous referees for their extremely useful comments and corrections which greatly improved the paper.

PY - 2019/11

Y1 - 2019/11

N2 - We study the poset of all unlabelled graphs with if H occurs as an induced subgraph in G. We present some general results on the Möbius function of intervals of and some results for specific classes of graphs. This includes a case where the Möbius function is given by the Catalan numbers, which we prove using discrete Morse theory, and another case where it equals the Fibonacci numbers, therefore showing that the Möbius function is unbounded. A classification of the disconnected intervals of is presented, which gives a large class of non-shellable intervals. We also present several conjectures on the structure of .

AB - We study the poset of all unlabelled graphs with if H occurs as an induced subgraph in G. We present some general results on the Möbius function of intervals of and some results for specific classes of graphs. This includes a case where the Möbius function is given by the Catalan numbers, which we prove using discrete Morse theory, and another case where it equals the Fibonacci numbers, therefore showing that the Möbius function is unbounded. A classification of the disconnected intervals of is presented, which gives a large class of non-shellable intervals. We also present several conjectures on the structure of .

KW - Graph containment

KW - Posets

KW - Möbius function

KW - MOBIUS FUNCTION

KW - Mobius function

UR - http://www.scopus.com/inward/record.url?scp=85068251243&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/poset-graphs-ordered-induced-containment

UR - https://abdn.pure.elsevier.com/en/en/researchoutput/the-poset-of-graphs-ordered-by-induced-containment(85be492f-1a93-45cf-93cb-00b848cfd54b).html

U2 - 10.1016/j.jcta.2019.06.009

DO - 10.1016/j.jcta.2019.06.009

M3 - Article

VL - 168

SP - 348

EP - 373

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

SN - 0097-3165

ER -