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• W3009686100 abstract "Let $k geq 2$ be an integer. Kouider and Lonc proved that the vertex set of every graph $G$ with $n geq n_0(k)$ vertices and minimum degree at least $n/k$ can be covered by $k - 1$ cycles. Our main result states that for every $alpha > 0$ and $p = p(n) in (0, 1]$, the same conclusion holds for graphs $G$ with minimum degree $(1/k + alpha)np$ that are sparse in the sense that [ e_G(X,Y) leq p|X||Y| + o(npsqrt{|X||Y|}/log^3 n) qquad forall X,Ysubseteq V(G). ] In particular, this allows us to determine the local resilience of random and pseudorandom graphs with respect to having a vertex cover by a fixed number of cycles. The proof uses a version of the absorbing method in sparse expander graphs." @default.
• W3009686100 created "2020-03-13" @default.
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• W3009686100 date "2020-03-06" @default.
• W3009686100 modified "2023-09-27" @default.
• W3009686100 title "Covering cycles in sparse graphs" @default.
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