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- W2034163816 abstract "In 1978, Bollobás and Eldridge [5] made the following two conjectures.(C1) There exists an absolute constant $c>0$ such that, if k is a positive integer and $G_1$ and $G_2$ are graphs of order n such that $Delta(G_1),Delta(G_2)leq n-k$ and $e(G_1),e(G_2)leq ck n$, then the graphs $G_1$ and $G_2$ pack.(C2) For all $0<alpha<1/2$ and $0<c<sqrt{1/8}$, there exists an $n_0=n_0(alpha,c)$ such that, if $G_1$ and $G_2$ are graphs of order $n>n_0$ satisfying $e(G_1)leq alpha n$ and $e(G_2)leq csqrt{n^3/ alpha}$, then the graphs $G_1$ and $G_2$ pack. Conjecture (C2) was proved by Brandt [6]. In the present paper we disprove (C1) and prove an analogue of (C2) for $1/2leq alpha<1$. We also give sufficient conditions for simultaneous packings of about $sqrt{n}/4$ sparse graphs." @default.
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- W2034163816 date "2005-10-11" @default.
- W2034163816 modified "2023-09-27" @default.
- W2034163816 title "On Two Conjectures on Packing of Graphs" @default.
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- W2034163816 doi "https://doi.org/10.1017/s0963548305006887" @default.
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