Results 91 to 100 of about 28,564 (220)
Rainbow Connection Number of Dense Graphs
Discussiones Mathematicae Graph Theory, 2013 An edge-colored graph G is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to ...
Li Xueliang +2 more
doaj +1 more source
Thinning to Improve Two‐Sample Discrepancy
Random Structures &Algorithms, Volume 68, Issue 2, March 2026.ABSTRACT The discrepancy between two independent samples X1,…,Xn$$ {X}_1,\dots, {X}_n $$ and Y1,…,Yn$$ {Y}_1,\dots, {Y}_n $$ drawn from the same distribution on ℝd$$ {\mathbb{R}}^d $$ typically has order O(n)$$ O\left(\sqrt{n}\right) $$ even in one dimension.
Gleb Smirnov, Roman Vershynin
wiley +1 more source
Solving a Random Asymmetric TSP Exactly in Quasi‐Polynomial Time W.H.P.
Random Structures &Algorithms, Volume 68, Issue 2, March 2026.ABSTRACT Let the costs C(i,j)$$ C\left(i,j\right) $$ for an instance of the Asymmetric Traveling Salesperson Problem (ATSP) be independent copies of a nonnegative random variable C$$ C $$ from a class of distributions that include the uniform [0,1]$$ \left[0,1\right] $$ distribution and the exponential mean 1 distribution with mean 1.
Tolson Bell, Alan M. Frieze
wiley +1 more source
Universality for Graphs of Bounded Degeneracy
Random Structures &Algorithms, Volume 68, Issue 2, March 2026.ABSTRACT Given a family ℋ$$ \mathscr{H} $$ of graphs, a graph G$$ G $$ is called ℋ$$ \mathscr{H} $$‐universal if G$$ G $$ contains every graph of ℋ$$ \mathscr{H} $$ as a subgraph. Following the extensive research on universal graphs of small size for bounded‐degree graphs, Alon asked what is the minimum number of edges that a graph must have to be ...
Peter Allen +2 more
wiley +1 more source
Random Structures &Algorithms, Volume 68, Issue 2, March 2026.ABSTRACT Let G$$ G $$ be a Dirac graph, and let S$$ S $$ be a vertex subset of G$$ G $$, chosen uniformly at random. How likely is the induced subgraph G[S]$$ G\left[S\right] $$ to be Hamiltonian? This question, proposed by Erdős and Faudree in 1996, was recently resolved by Draganić, Keevash, and Müyesser, in the setting of graphs.
Zach Hunter +3 more
wiley +1 more source
On quantum ergodicity for higher‐dimensional cat maps modulo prime powers
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract A discrete model of quantum ergodicity of linear maps generated by symplectic matrices A∈Sp(2d,Z)$A \in \operatorname{Sp}(2d,{\mathbb {Z}})$ modulo an integer N⩾1$N\geqslant 1$, has been studied for d=1$d=1$ and almost all N$N$ by Kurlberg and Rudnick (2001, Comm. Math. Phys., 222, 201–227).
Subham Bhakta, Igor E. Shparlinski
wiley +1 more source
Zarankiewicz bounds from distal regularity lemma
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract Since Kővári, Sós and Turán proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricting to particular classes of graphs. In 2017, Fox, Pach, Sheffer, Suk and Zahl proved better bounds for semialgebraic binary relations, and this work was extended by Do in
Mervyn Tong
wiley +1 more source
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Heilbronn's triangle problem is a classical question in discrete geometry. It asks to determine the smallest number Δ=Δ(N)$\Delta = \Delta (N)$ for which every collection in N$N$ points in the unit square spans a triangle with area at most Δ$\Delta$.
Dmitrii Zakharov
wiley +1 more source
Determinacy on the edge of second‐order arithmetic, I
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract This is the first of two articles on the strength of m$m{}$‐Σ30$\bm{\Sigma }^0_3{}$‐determinacy for m∈N$m\in \mathbb {N}$, the strongest theories of determinacy contained in Hilbert's second‐order arithmetic (Z2)$(Z_2)$. In this article, we refute two natural conjectures on the strength of these principles in terms of inductive definability ...
J. P. Aguilera, P. D. Welch
wiley +1 more source
BarekengThe rainbow connection was first introduced by Chartrand in 2006 and then in 2009 Krivelevich and Yuster first time introduced the rainbow vertex connection. Let graph be a connected graph.
Muhammad Ilham Nurfaizi Annadhifi +3 more
doaj +1 more source