Results 11 to 20 of about 51 (51)
On the Restricted Size Ramsey Number Involving a Path P3
Discussiones Mathematicae Graph Theory, 2019 For any pair of graphs G and H, both the size Ramsey number ̂r(G,H) and the restricted size Ramsey number r*(G,H) are bounded above by the size of the complete graph with order equals to the Ramsey number r(G,H), and bounded below by e(G) + e(H) − 1 ...
Silaban Denny Riama +2 more
doaj +1 more source
A monotone path in an edge‐ordered graph
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 2, Page 315-320, 1987., 1986 An edge‐ordered graph is an ordered pair (G, f), where G is a graph and f is a bijective function, f : E(G) → {1, 2, …, |E(G)|}. A monotone path of length k in (G, f) is a simple path Pk+1 : v1v2 … vk+1 in G such that either f({vi, vi+1}) < f({vi+1, vi+2}) or f({vi, vi+1}) > f({vi+1, vi}) for i = 1, 2, …, k − 1.
A. Bialostocki, Y. Roditty
wiley +1 more source
Proof of a conjecture of Galvin
Forum of Mathematics, Pi, 2020 We prove that if the set of unordered pairs of real numbers is coloured by finitely many colours, there is a set of reals homeomorphic to the rationals whose pairs have at most two colours.
Dilip Raghavan, Stevo Todorcevic
doaj +1 more source
A Note on Upper Bounds for Some Generalized Folkman Numbers
Discussiones Mathematicae Graph Theory, 2019 We present some new constructive upper bounds based on product graphs for generalized vertex Folkman numbers. They lead to new upper bounds for some special cases of generalized edge Folkman numbers, including the cases Fe(K3, K4 − e; K5) ≤ 27 and Fe(K4 −
Xu Xiaodong +2 more
doaj +1 more source
A Note on Lower Bounds for Induced Ramsey Numbers
Discussiones Mathematicae Graph Theory, 2019 We say that a graph F strongly arrows a pair of graphs (G,H) and write F →ind$\mathop \to \limits^{{\rm{ind}}} $(G,H) if any 2-coloring of its edges with red and blue leads to either a red G or a blue H appearing as induced subgraphs of F.
Gorgol Izolda
doaj +1 more source
Ramsey Properties of Random Graphs and Folkman Numbers
Discussiones Mathematicae Graph Theory, 2017 For two graphs, G and F, and an integer r ≥ 2 we write G → (F)r if every r-coloring of the edges of G results in a monochromatic copy of F. In 1995, the first two authors established a threshold edge probability for the Ramsey property G(n, p) → (F)r ...
Rödl Vojtěch +2 more
doaj +1 more source
A Note on the Ramsey Number of Even Wheels Versus Stars
Discussiones Mathematicae Graph Theory, 2018 For two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N, such that for any graph on N vertices, either G contains G1 or Ḡ contains G2. Let Sn be a star of order n and Wm be a wheel of order m + 1.
Haghi Sh., Maimani H.R.
doaj +1 more source
Another View of Bipartite Ramsey Numbers
Discussiones Mathematicae Graph Theory, 2018 For bipartite graphs F and H and a positive integer s, the s-bipartite Ramsey number BRs(F,H) of F and H is the smallest integer t with t ≥ s such that every red-blue coloring of Ks,t results in a red F or a blue H.
Bi Zhenming, Chartrand Gary, Zhang Ping
doaj +1 more source
MONOID ACTIONS AND ULTRAFILTER METHODS IN RAMSEY THEORY
Forum of Mathematics, Sigma, 2019 First, we prove a theorem on dynamics of actions of monoids by endomorphisms of semigroups. Second, we introduce algebraic structures suitable for formalizing infinitary Ramsey statements and prove a theorem that such statements are implied by the ...
SŁAWOMIR SOLECKI
doaj +1 more source
Density of monochromatic infinite subgraphs II
Forum of Mathematics, SigmaIn 1967, Gerencsér and Gyárfás [16] proved a result which is considered the starting point of graph-Ramsey theory: In every 2-coloring of $K_n$ , there is a monochromatic path on $\lceil (2n+1)/3\rceil $ vertices, and this is best possible ...
Jan Corsten +2 more
doaj +1 more source