Decomposing Random Graphs into Few Cycles and Edges
نویسندگان
چکیده
Over 50 years ago, Erdős and Gallai conjectured that the edges of every graph on n vertices can be decomposed into O(n) cycles and edges. Among other results, Conlon, Fox and Sudakov recently proved that this holds for the random graph G(n, p) with probability approaching 1 as n → ∞. In this paper we show that for most edge probabilities G(n, p) can be decomposed into a union of n4 + np 2 + o(n) cycles and edges whp. This result is asymptotically tight. AMS Subject Classification: 05C38, 05C80.
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عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 24 شماره
صفحات -
تاریخ انتشار 2015