@article {
author = {N. Iradmusa, Moharram},
title = {Counterexamples to a conjecture on matching Kneser graphs},
journal = {Transactions on Combinatorics},
volume = {12},
number = {3},
pages = {172-173},
year = {2023},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2022.132638.1961},
abstract = {Let $G$ be a graph and $r\in\mathbb{N}$. The matching Kneser graph $\textsf{KG}(G, rK_2)$ is a graph whose vertex set is the set of $r$-matchings in $G$ and two vertices are adjacent if their corresponding matchings are edge-disjoint. In [M. Alishahi and H. Hajiabolhassan, On the Chromatic Number of Matching Kneser Graphs, Combin. Probab. and Comput., 29, No. 1 (2020), 1--21] it was conjectured that for any connected graph $G$ and positive integer $r\geq 2$, the chromatic number of $\textsf{KG}(G, rK_2)$ is equal to $|E(G)|-\textsf{ex}(G,rK_2)$, where $\textsf{ex}(G,rK_2)$ denotes the largest number of edges in $G$ avoiding a matching of size $r$. In this note, we show that the conjecture is not true for snarks.},
keywords = {matching Kneser graph,snarks,chromatic number},
url = {https://toc.ui.ac.ir/article_26847.html},
eprint = {https://toc.ui.ac.ir/article_26847_9307b1b5b45d7de0418b8b8b2bb530fc.pdf}
}