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The Homotopy Type of the Independence Complex of Graphs with No Induced Cycles of Length Divisible by 3

  • 2021
  • OriginalPaper
  • Chapter
Published in:
Author
Jinha Kim
Published in
Extended Abstracts EuroComb 2021
Publisher
Springer International Publishing

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Abstract

The chapter delves into the homotopy type of the independence complex of graphs that contain no induced cycles of length divisible by 3, known as ternary graphs. The main theorem establishes that a graph is ternary if and only if every induced subgraph has an independence complex that is contractible or homotopy equivalent to a sphere. This result is motivated by a conjecture by Kalai and Meshulam and builds upon previous work by Zhang and Wu. The text also explores the topological background and useful lemmas to determine the homotopy type of independence complexes, making it a valuable resource for researchers in algebraic topology and graph theory.
AI Generated

This summary of the content was generated with the help of AI.

J. Kim—This work was supported by the Institute for Basic Science (IBS-R029-C1).

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previous chapter Bounds on Half Graph Orders in Powers of Sparse Graphs
next chapter The Maximum Number of Paths of Length Three in a Planar Graph
Title
The Homotopy Type of the Independence Complex of Graphs with No Induced Cycles of Length Divisible by 3
Author
Jinha Kim
Copyright Year
2021
Book
Extended Abstracts EuroComb 2021

Print ISBN: 978-3-030-83822-5

Electronic ISBN: 978-3-030-83823-2

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-83823-2_40
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