Sprinkling a Few Random Edges Doubles the Power
نویسندگان
چکیده
Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 3 April 2019Accepted: 16 October 2020Published online: 17 May 2021Keywordsextremal graph theory, random graphs, HamiltonicityAMS Subject Headings05C35, 05C80Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Industrial and Applied MathematicsCODEN: sjdmec
منابع مشابه
Decomposing Random Graphs into Few Cycles and Edges
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...
متن کاملColoring uniform hypergraphs with few edges
A hypergraph is b-simple if no two distinct edges share more than b vertices. Let m(r, t, g) denote the minimum number of edges in an r-uniform non-t-colorable hypergraph of girth at least g. Erdős and Lovász proved that m(r, t, 3) ≥ t 2(r−2) 16r(r − 1)2 and m(r, t, g) ≤ 4 · 20g−1r3g−5t(g−1)(r+1). A result of Szabó improves the lower bound by a factor of r2− for sufficiently large r. We improve...
متن کاملColour-critical graphs with few edges
A graph G is called k-critical if G is k-chromatic but every proper subgraph of G has chromatic number at most k 1. In this paper the following result is proved. If G is a k-critical graph (k>~4) on n vertices, then 21E(G)I>(k 1)n ÷ ((k 3)/(k 2 3))n + k 4 where n>~k + 2 and n ~ 2 k 1. This improves earlier bounds established by Dirac (1957) and Gallai (1963). (~) 1998 Elsevier Science B.V. All ...
متن کاملObtaining Planarity by Contracting Few Edges
The Planar Contraction problem is to test whether a given graph can be made planar by using at most k edge contractions. This problem is known to be NP-complete. We show that it is fixedparameter tractable when parameterized by k.
متن کاملColor-Critical Graphs and Hypergraphs with Few Edges: A Survey
A hypergraph is color-critical if deleting any edge or vertex reduces the chromatic number; a color-critical hypergraph with chromatic number k is k-critical. Every k-chromatic hypergraph contains a k-critical hypergraph, so one can study chromatic number by studying the structure of k-critical (hyper)graphs. There is vast literature on k-critical graphs and hypergraphs. Many references can be ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2021
ISSN: ['1095-7146', '0895-4801']
DOI: https://doi.org/10.1137/19m125412x