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 -