Sectionable Tournaments: their Topology and Coloring
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Dosyalar
Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
We provide a detailed study of topological and combinatorial properties of sectionable tournaments. This class forms an inductively constructed family of tournaments grounded over simply disconnected tournaments, those tournaments whose fundamental groups of acyclic complexes are non-trivial. When T is a sectionable tournament, we fully describe the cell-structure of its acyclic complex Acy(T) by using the adapted machinery of discrete Morse theory for acyclic complexes of tournaments. In the combinatorial side, we demonstrate that the dimension of the complex Acy(T) has a role to play. We prove that if T is a (2r + 1)-sectionable tournament and d is the dimension of Acy(T), then the (acyclic) chromatic number of T satisfies chi(T)<= 2(2-1/(r+1))(log(d+1))-1 where the logarithm has two as its base.
Açıklama
Anahtar Kelimeler
Tournaments; Simplicial Complexes; Discrete Morse Theory; Coloring
Kaynak
Order-A Journal on The Theory of Ordered Sets and Its Applications
WoS Q Değeri
Q4
Scopus Q Değeri
Q3
