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11.
Anton Kotzig 《Journal of Combinatorial Theory, Series B》1977,22(1):26-30
It will be proved that the number of vertices of each component of the change-graph of two edge-colorings of an arbitrary planar cubic graph is even (here a change-graph is the subgraph containing exactly those edges having different colors in the considered two edge-colorings and moreover only those vertices which are incident with at least one of these edges). 相似文献
12.
Anton Kotzig 《Journal of Graph Theory》1979,3(1):23-34
Let G1, G2…, Gn be regular graphs and H be the Cartesian product of these graphs (H = G1 × G2 × … × Gn). The following will be proved: If the set {G1, G2…, Gn} has at leat one of the following properties: (*) for at leat one i ? {1, 2,…, n}, there exists a 1-factorization of Gi or (**) there exists at least two numbers i and j such that 1 ≤ i < j ≤ n and both the Graphs Gi and Gj contain at least one 1-factor, then there exists a 1-factorization of H. Further results: Let F be a cycle of length greater than three and let G be an arbitrary cubic graph. Then there exists a 1-factorization of the 5-regular graph H = F × G. The last result shows that neither (*) nor (**) is a necessary condition for the existence of a 1-factorization of a Cartesian product of regular graphs. 相似文献
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