PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 33(47), pp. 193--196 (1983)
1-FACTORIZATION OF THE COMPOSITION OF REGULAR GRAPHS
Tomaz Pisanski, John Shawe-Taylor, Bojan MoharDepartment of Mathematics, University of Ljubljana 61000 Ljubljana, Yugoslaviaa
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.
Keywords: Regular graph, edge-colouring, 1-factorization
Classification (MSC2000): 05C15
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts