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1-factorisation of the Composition of Regular Graphs

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

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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 $Gotimes H$ is 1-factorable, if at least one of two graphs is 1-factorable. This result in turn implies that the strong tensor product $Gotimes' H$ is 1-factorable, if $G$ is 1-factorable

Type:Article
Title:1-factorisation of the Composition of Regular Graphs
Keywords:1-factorization, edge-colouring, graph, Regular graph
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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