The Morse complex of the wedge of two extended star graphs and a path
Combinatorics
2025-11-11 v2
Abstract
In the work of C. Donovan and N. A. Scoville, the homotopy type of the Morse complex of the extended star graph which is obtained as the one-point union of n paths of length 2 was determined by using star clusters and Cluster Lemma. In this paper, we determine the homotopy type of the Morse complex of extended star graph consisting of a path of length 1 and n paths of length 2 by using strong collapses and Hasse diagram. Furthermore, we compute the homotopy type of the graph obtained by attaching the center vertices of two extended star graphs to different endpoints of a path by using star clusters and the Cluster Lemma.
Cite
@article{arxiv.2510.26176,
title = {The Morse complex of the wedge of two extended star graphs and a path},
author = {Shuma Komatsu},
journal= {arXiv preprint arXiv:2510.26176},
year = {2025}
}