Author:
Beineke Lowell W.,Guy Richard K.
Abstract
The coarseness, c(G), of a graph G is the maximum number of edge-disjoint, non-planar graphs whose union is G. The coarseness of the complete graph has been investigated elsewhere (1; 2). We consider the coarseness of the complete bipartite, or 2-coloured, graph, Km,n, consisting of sets of mand nvertices, each member of one set being joined by an edge to each member of the other. No members of one set are joined to each other.Our results are summarized in the following theorem, where square brackets denote “integer part”.THEOREM. If m= 3p + d, 0 ≦ d≦ 2, and n = 3q + e, 0 ≦ e ≦ 2, then for d = 0 or 1 and e = 0 or 1,1
Publisher
Canadian Mathematical Society
Cited by
9 articles.
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1. Richard Kenneth Guy, 1916–2020;Bulletin of the London Mathematical Society;2022-02
2. Nordhaus–Gaddum results for genus;Discrete Mathematics;2013-03
3. Non-planar core reduction of graphs;Discrete Mathematics;2009-04
4. References;North-Holland Mathematics Studies;2001
5. Imbedding Problems in Graph Theory;North-Holland Mathematics Studies;2001