The poset of graphs ordered by induced containment

Jason P. Smith

doi:10.1016/j.jcta.2019.06.009

The poset of graphs ordered by induced containment

Jason P. Smith (Corresponding Author)

Mathematical Science

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

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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 language	English
Pages (from-to)	348-373
Number of pages	26
Journal	Journal of Combinatorial Theory, Series A
Volume	168
Early online date	4 Jul 2019
DOIs	https://doi.org/10.1016/j.jcta.2019.06.009
Publication status	Published - Nov 2019

Keywords

Graph containment
Posets
Möbius function
MOBIUS FUNCTION
Mobius function

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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 .",

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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 .

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KW - Möbius function

KW - MOBIUS FUNCTION

KW - Mobius function

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The poset of graphs ordered by induced containment

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Keywords

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