The Topological Connectivity of the Independence Complex of Circular-Arc Graphs

Yousef Mathkal Abd Algani

Research output: Contribution to journalArticlepeer-review

Abstract

Let us denoted the topological connectivity of a simplicial complex C plus 2 by η(C). Let ψ be a function from class of graphs to the set of positive integers together with ∞. Suppose ψ satisfies the following properties: (formula presented) (where G − e is obtained from G by the removal of the edge e), and ψ(G − N({x, y})) ≥ ψ(G) − 1 η(I (G)) ≥ ψ(G) (where (G − N({x, y})) is obtained from G by the removal of all neighbors of x and y (including, of course, x and y themselves). Let us denoted the maximal function satisfying the conditions above by ψ0. Berger [3] prove the following conjecture: η(I (G)) = ψ0 (G) for trees and completements of chordal graphs. Kawamura [2] proved conjecture, for chordal graphs. Berger [3] proved Conjecture for trees and completements of chordal graphs. In this article I proved the following theorem: Let G be a circular-arc graph G if ψ0 (G) ≤ 2 then η(I (G)) ≤ 2. Prior the attempt to verify the previously mentioned cases, we need a few preparations which will be discussed in the introduction.

Original languageEnglish
Pages (from-to)159-169
Number of pages11
JournalUniversal Journal of Mathematics and Applications
Volume2
Issue number4
DOIs
StatePublished - 26 Dec 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019, Emrah Evren KARA. All rights reserved.

Keywords

  • Circular-Arc Graphs
  • Independence Complex
  • Topological Connectivity

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