1-factorisation of the Composition of Regular Graphs
1-factorisation of the Composition of Regular Graphs
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.
Regular graph, edge-colouring, 1-factorization
193-196
Pisanski, T.
09317670-2c1d-43c1-bba4-331e50f540a5
Shawe-Taylor, J.
c32d0ee4-b422-491f-8c28-78663851d6db
Mohar, B.
f2acae5d-010f-48f6-a425-4ff5d23487ad
1983
Pisanski, T.
09317670-2c1d-43c1-bba4-331e50f540a5
Shawe-Taylor, J.
c32d0ee4-b422-491f-8c28-78663851d6db
Mohar, B.
f2acae5d-010f-48f6-a425-4ff5d23487ad
Pisanski, T., Shawe-Taylor, J. and Mohar, B.
(1983)
1-factorisation of the Composition of Regular Graphs.
Publications de l'Institut Mathématique, 33 (47), .
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.
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1FactorisationOfTheCompositionOfRegularGraphs.pdf
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Published date: 1983
Keywords:
Regular graph, edge-colouring, 1-factorization
Organisations:
Electronics & Computer Science
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Local EPrints ID: 259862
URI: http://eprints.soton.ac.uk/id/eprint/259862
ISSN: 0350-1302
PURE UUID: da978eae-42b7-476c-8075-6d999b1fcd69
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Date deposited: 31 Aug 2004
Last modified: 14 Mar 2024 06:29
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Contributors
Author:
T. Pisanski
Author:
J. Shawe-Taylor
Author:
B. Mohar
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