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- W2997367087 abstract "The weak minor G of a graph G is the graph obtained from G by a sequence of edge-contraction operations on G. A weak-minor-closed family of upper embeddable graphs is a set G of upper embeddable graphs that for each graph G in G ,e very weak minor ofG is also in G. Up to now, there are few results providing the necessary and sufficient conditions for characterizing upper embeddability of graphs. In this paper, we study the relation between the vertex splitting operation and the upper embeddability of graphs; provide not only a necessary and sufficient condition for characterizing upper embeddability of graphs, but also a way to construct weak-minor-closed family of upper embeddable graphs from the bouquet of circles; and extend a result in (J. Graph Theory, 1981, 5(2): 205-207). In addition, the algorithm complex of determining the upper embeddability of a graph can be reduced much by the results obtained in this paper." @default.
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- W2997367087 date "2014-09-05" @default.
- W2997367087 modified "2023-09-24" @default.
- W2997367087 title "Vertex Splitting and Upper Embeddable Graphs" @default.
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- W2997367087 doi "https://doi.org/10.11845/sxjz.2012179b" @default.
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