Geodesic
Sortable simplicial complexes and \(t\)-independence ideals of proper interval graphs
Jürgen Herzog1 ; Fahimeh Khosh-Ahang2 ; Somayeh Moradi2 ; Masoomeh Rahimbeigi3
1University of Duisburg-Essen
2Ilam University
3University of Kurdistan
The electronic journal of combinatorics, Tome 27 (2020) no. 1
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We introduce the notion of sortability and $t$-sortability for a simplicial complex and study the graphs for which their independence complexes are either sortable or $t$-sortable. We show that the proper interval graphs are precisely the graphs whose independence complex is sortable. By using this characterization, we show that the ideal generated by all squarefree monomials corresponding to independent sets of vertices of $G$ of size $t$ (for a given positive integer $t$) has the strong persistence property, when $G$ is a proper interval graph. Moreover, all of its powers have linear quotients.
DOI : 10.37236/8860
Classification : 13F20, 05E45
Mots-clés : independence complex, interval graph, proper graph, sortable simplicial complex

Jürgen Herzog  1   ; Fahimeh Khosh-Ahang  2   ; Somayeh Moradi  2   ; Masoomeh Rahimbeigi  3

1 University of Duisburg-Essen
2 Ilam University
3 University of Kurdistan 
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     title = {Sortable simplicial complexes and \(t\)-independence ideals of proper interval graphs},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {1},
     doi = {10.37236/8860},
     zbl = {1460.13031},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8860/}
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Jürgen Herzog; Fahimeh Khosh-Ahang; Somayeh Moradi; Masoomeh Rahimbeigi. Sortable simplicial complexes and \(t\)-independence ideals of proper interval graphs. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8860

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