# 1-factorisation of the Composition of Regular Graphs

Pisanski, T., Shawe-Taylor, J. and Mohar, B. (1983) 1-factorisation of the Composition of Regular Graphs. Publications de l'Institut Mathématique, 33, (47), 193-196.

## Description/Abstract

1-factorability of the composition of graphs is studied. The followings sufficient conditions are proved: $G[H]$ is 1-factorable if $G$ and $H$ are regular and at least one of the following holds: (i) Graphs $G$ and $H$ both contain a 1-factor, (ii) $G$ is 1-factorable (iii) $H$ is 1-factorable. It is also shown that the tensor product $G\otimes H$ is 1-factorable, if at least one of two graphs is 1-factorable. This result in turn implies that the strong tensor product $G\otimes' H$ is 1-factorable, if $G$ is 1-factorable.

Item Type: Article 0350-1302 http://emis.math.ecnu.edu.cn/j...47/28.html Regular graph, edge-colouring, 1-factorization Faculty of Physical Sciences and Engineering > Electronics and Computer Science 259862 31 Aug 2004 27 Mar 2014 20:02 Google Scholar http://eprints.soton.ac.uk/id/eprint/259862