Bandwidth theorem for random graphs
نویسندگان
چکیده
منابع مشابه
Bandwidth theorem for random graphs
A graph G is said to have bandwidth at most b, if there exists a labeling of the vertices by 1, 2, . . . , n, so that |i − j| ≤ b whenever {i, j} is an edge of G. Recently, Böttcher, Schacht, and Taraz verified a conjecture of Bollobás and Komlós which says that for every positive r,∆, γ, there exists β such that if H is an n-vertex r-chromatic graph with maximum degree at most ∆ which has band...
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A classical theorem of Dirac from 1952 asserts that every graph on n vertices with minimum degree at least dn/2e is Hamiltonian. In this paper we extend this result to random graphs. Motivated by the study of resilience of random graph properties we prove that if p log n/n, then a.a.s. every subgraph ofG(n, p) with minimum degree at least (1/2+o(1))np is Hamiltonian. Our result improves on prev...
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For a graph G, denote by t(G) (resp. b(G)) the maximum size of a triangle-free (resp. bipartite) subgraph of G. Of course t(G) ≥ b(G) for any G, and a classic result of Mantel from 1907 (the first case of Turán’s Theorem) says that equality holds for complete graphs. A natural question, first considered by Babai, Simonovits and Spencer about 20 years ago is, when (i.e. for what p = p(n)) is the...
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of a thesis submitted to the Faculty of the Graduate School of Emory University in partial fulfillment of the requirements of the degree of Master of Science Department of Mathematics and Computer Science
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2012
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2011.03.002