A $C_{4}$-decomposition of the $\lambda$-fold line graph of $K_{m,n}$

Yifan Zhao; Yulong Wei; Weihua Yang

A $C_{4}$-decomposition of the $\lambda$-fold line graph of $K_{m,n}$

Combinatorics 2022-05-12 v1

Authors: Yifan Zhao , Yulong Wei , Weihua Yang

Abstract

The small cycle decompositions of line graph ( $\lambda$ -fold line graph) of complete graphs and complete bipartite graphs are studied by many papers. In particular, Colby and Rodger obtained necessary and sufficient conditions for the existence of a $C_{4}$ -decomposition of the $\lambda$ -fold line graph of $K_{n}$ , and Ganesamurthy and Paulraja completely determined the values of $n$ and $\lambda$ for which the $\lambda$ -fold line graph of $K_{n}$ has a $C_{5}$ -decomposition. In this paper, we obtain the necessary and sufficient condition for the existence of a $C_{4}$ -decomposition of the $\lambda$ -fold line graph of $K_{m,n}$ .

Keywords

cycle decomposition line graph complete bipartite graph necessary and sufficient condition graph theory

Cite

@article{arxiv.2205.05117,
  title  = {A $C_{4}$-decomposition of the $\lambda$-fold line graph of $K_{m,n}$},
  author = {Yifan Zhao and Yulong Wei and Weihua Yang},
  journal= {arXiv preprint arXiv:2205.05117},
  year   = {2022}
}

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A $C_{4}$-decomposition of the $\lambda$-fold line graph of $K_{m,n}$

Abstract

Keywords

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