PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 33(47), pp. 193196 (1983) 

1FACTORIZATION OF THE COMPOSITION OF REGULAR GRAPHSTomaz Pisanski, John ShaweTaylor, Bojan MoharDepartment of Mathematics, University of Ljubljana 61000 Ljubljana, YugoslaviaaAbstract: 1factorability of the composition of graphs is studied. The followings sufficient conditions are proved: $G[H]$ is 1factorable if $G$ and $H$ are regular and at least one of the following holds: (i) Graphs $G$ and $H$ both contain a 1factor, (ii) $G$ is 1factorable (iii) $H$ is 1factorable. It is also shown that the tensor product $G\otimes H$ is 1factorable, if at least one of two graphs is 1factorable. This result in turn implies that the strong tensor product $G\otimes' H$ is 1factorable, if $G$ is 1factorable. Keywords: Regular graph, edgecolouring, 1factorization Classification (MSC2000): 05C15 Full text of the article:
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