Abstract
We give a polynomial time randomized algorithm that, on receiving as input a pair (H,G) of n-vertex graphs, searches for an embedding of H into G. If H has bounded maximum degree and G is suitably dense and pseudorandom, then the algorithm succeeds with high probability. Our algorithm proves that, for every integer d ≥ 3 and suitable constant C = C d , as n → ∞, asymptotically almost all graphs with n vertices and \(\lfloor Cn^{2-1/d}\log^{1/d}n\rfloor\) edges contain as subgraphs all graphs with n vertices and maximum degree at most d.
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Dellamonica, D., Kohayakawa, Y., Rödl, V., Ruciński, A. (2012). An Improved Upper Bound on the Density of Universal Random Graphs. In: Fernández-Baca, D. (eds) LATIN 2012: Theoretical Informatics. LATIN 2012. Lecture Notes in Computer Science, vol 7256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29344-3_20
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DOI: https://doi.org/10.1007/978-3-642-29344-3_20
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