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Upper embeddable factorizations of graphs. (English) Zbl 0583.05045
Let G be a graph (possibly with multiple edges and loops). A sequence \((G_ 1,\ldots,G_ n)\), where \(n\geq 1\), is referred to as an upper embeddable n-factorization of G if \(G_ 1,\ldots,G_ n\) are upper embeddable spanning subgraphs of G, and each edge of G belongs to exactly one of the graphs \(G_ 1,\ldots,G_ n\). The paper gives a necessary and sufficient condition for a graph to have an upper embeddable n- factorization (Theorem 2). The proof is partially based on a generalization of methods used by the author in his paper on the maximum genus of a graph [ibid. 31(106), 604-613 (1981; Zbl 0482.05034)].
MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C10 Planar graphs; geometric and topological aspects of graph theory
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References:
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