Topology of Clique Complexes of Line Graphs
Combinatorics
2022-04-29 v2 Algebraic Topology
Abstract
The clique complex of a graph G is a simplicial complex whose simplices are all the cliques of G, and the line graph L(G) of G is a graph whose vertices are the edges of G and the edges of L(G) are incident edges of G. In this article, we determine the homotopy type of the clique complexes of line graphs for several classes of graphs including triangle-free graphs, chordal graphs, complete multipartite graphs, wheel-free graphs, and 4-regular circulant graphs. We also give a closed form formula for the homotopy type of these complexes in several cases.
Keywords
Cite
@article{arxiv.2009.12130,
title = {Topology of Clique Complexes of Line Graphs},
author = {Shuchita Goyal and Samir Shukla and Anurag Singh},
journal= {arXiv preprint arXiv:2009.12130},
year = {2022}
}
Comments
Version 2: Section 3 and Section 5 have been merged, and the proofs have been modified incorporating the referee's comments. To appear in the Art of Discrete and Applied Mathematics