On the genus of joins and compositions of graphs

We will use a surgical technique to imbed the composition graph G[ H] when G has minimum degree 2 and H has even order. This imbedding is shown to be minimal when G is triangle-free. Along the way, we construct genus imbeddings of the join G + H when both factors have even order, G is empty or 1-reg...

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Bibliographic Details
Published in:Discrete mathematics 1998, Vol.178 (1), p.25-50
Main Author: Craft, David L.
Format: Article
Language:English
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Summary:We will use a surgical technique to imbed the composition graph G[ H] when G has minimum degree 2 and H has even order. This imbedding is shown to be minimal when G is triangle-free. Along the way, we construct genus imbeddings of the join G + H when both factors have even order, G is empty or 1-regular, and G has order at least twice that of H. Variants and applications to specific graphs, such as complete tripartite graphs, are given.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(97)81815-8