Abstract
A labelled coloured bipartite graph, of LCBG, is a bipartite (simple) graph whose vertices have been 2-coloured and the vertices of each colour labelled independently. It is shown that for fixed r⩾3 the proportion of r-regular LCBGs on 2n vertices which are r-connected approaches 1 as n → ∞. Also, fix r⩾3 and q>0; let g=max(4,2{q/(2(r−2))}). Then the numbers of the following types of r-regular LCBGs with 2n vertices are asymptotically equal as n → ∞: those with girth at least g; those which are cyclically-q-edge-connected; and those which are cyclically-q-vertex-connected.
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© 1983 Springer-Verlag
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Ellingham, M.N. (1983). The asymptotic connectivity of labelled coloured regular bipartite graphs. In: Casse, L.R.A. (eds) Combinatorial Mathematics X. Lecture Notes in Mathematics, vol 1036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071518
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DOI: https://doi.org/10.1007/BFb0071518
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