Geodesic
Erdős-Ko-Rado type theorems for simplicial complexes
Seyed Amin Seyed Fakhari1
1University of Tehran
The electronic journal of combinatorics, Tome 24 (2017) no. 2
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It is shown that every shifted simplicial complex $\Delta$ is EKR of type $(r,s)$, provided that the size of every facet of $\Delta$ is at least $(2s+1)r-s$. It is moreover proven that every $i$-near-cone simplicial complex is EKR of type $(r,i)$ if ${\rm depth}_{\mathbb{K}}\Delta\geq (2i+1)r-i-1$, for some field $\mathbb{K}$. Furthermore, we prove that if $G$ is a graph having at least $(2i+1)r-i$ connected components, including $i$ isolated vertices, then its independence simplicial complex $\Delta_G$ is EKR of type $(r,i)$. The results of this paper, generalize the main result of Frankl (2013).
DOI : 10.37236/6544
Classification : 05E45, 05D05, 05C70
Mots-clés : Erdős-Ko-Rado theorem, simplicial complex, matching number, algebraic shifting, \(i\)-near-cone

Seyed Amin Seyed Fakhari  1

1 University of Tehran 
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     author = {Seyed Amin Seyed Fakhari},
     title = {Erd\H{o}s-Ko-Rado type theorems for simplicial complexes},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {2},
     doi = {10.37236/6544},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/6544/}
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Seyed Amin Seyed Fakhari. Erdős-Ko-Rado type theorems for simplicial complexes. The electronic journal of combinatorics, Tome 24 (2017) no. 2. doi: 10.37236/6544

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