The Coarseness of the Complete Bipartite Graph
1969 ◽
Vol 21
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pp. 1086-1096
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Keyword(s):
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
1970 ◽
Vol 22
(5)
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pp. 1082-1096
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2006 ◽
Vol 15
(01)
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pp. 11-19
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Keyword(s):
1968 ◽
Vol 20
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pp. 888-894
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1964 ◽
Vol 7
(1)
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pp. 35-39
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Keyword(s):
2011 ◽
Vol 3
(2)
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pp. 321-329
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Keyword(s):
2018 ◽
Vol 106
(2)
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pp. 515-527
2015 ◽
Vol 07
(04)
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pp. 1550040
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Keyword(s):