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# 1-factorisation of the Composition of Regular Graphs

Record type: Article

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.

PDF 1FactorisationOfTheCompositionOfRegularGraphs.pdf - Other

## Citation

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

Published date: 1983
Keywords: Regular graph, edge-colouring, 1-factorization
Organisations: Electronics & Computer Science

## Identifiers

Local EPrints ID: 259862
URI: http://eprints.soton.ac.uk/id/eprint/259862
ISSN: 0350-1302
PURE UUID: da978eae-42b7-476c-8075-6d999b1fcd69

## Catalogue record

Date deposited: 31 Aug 2004

## Contributors

Author: T. Pisanski
Author: J. Shawe-Taylor
Author: B. Mohar