Geodesic
1-factorization of the Composition of Regular Graphs
Publications de l'Institut Mathématique, _N_S_33 (1983) no. 47, p. 193

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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.
Classification : 05C15
Keywords: Regular graph, edge-colouring, 1-factorization 
@article{PIM_1983_N_S_33_47_a27,
     author = {Toma\v{z} Pisanski and John Shawe-Taylor and Bojan Mohar},
     title = {1-factorization of the {Composition} of {Regular} {Graphs}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {193 },
     publisher = {mathdoc},
     volume = {_N_S_33},
     number = {47},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1983_N_S_33_47_a27/}
}
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Tomaž Pisanski; John Shawe-Taylor; Bojan Mohar. 1-factorization of the Composition of Regular Graphs. Publications de l'Institut Mathématique, _N_S_33 (1983) no. 47, p. 193 . http://geodesic.mathdoc.fr/item/PIM_1983_N_S_33_47_a27/