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Given two nonnegative integers n and k with n ≥ k > 1, a k-hypertournament on n vertices is a pair (V, A), where V is a set of vertices with |V | = n and A is a set of k-tuples of vertices, called arcs, such that for any k-subset S of V , A contains exactly one of the k! k-tuples whose entries belong to S. We show that a nondecreasing sequence (r1, r2, . .… (More)
Thomassen (J. Combin. Theory Ser. B 28, 1980, 142–163) proved that every strong tournament contains a vertex x such that each arc going out from x is contained in a Hamiltonian cycle. In this paper, we extend the result of Thomassen and prove that a strong tournament contains a vertex x such that every arc going out from x is pancyclic, and our proof yields… (More)
For two given graphsG1 andG2, the Ramsey numberR(G1,G2) is the smallest integer n such that for any graph G of order n, either G containsG1 or the complement of G containsG2. Let Pn denote a path of order n and Wm a wheel of order m+ 1. In this paper, we show that R(Pn,Wm)= 2n− 1 for m even and n m− 1 3 and R(Pn,Wm)= 3n− 2 for m odd and n m− 1 2. © 2004… (More)
We introduce a class of continuous maps f of a compact topological space X admitting inducing schemes of hyperbolic type and describe the associated tower constructions. We then establish a thermodynamic formalism, i.e., we describe a class of real-valued potential functions φ on X such that f possess a unique equilibrium measure μφ, associated to each φ,… (More)
Let Tn denote a tree of order n and Wm a wheel of order m + 1. Baskoro et al. conjectured in  that if Tn is not a star, then R(Tn,Wm) = 2n − 1 for m ≥ 6 even and n ≥ m− 1. We disprove the Conjecture in . In this paper, we determine R(Tn,W6) for n ≤ 8 which is the first step for us to determine R(Tn,W6) for any tree Tn.
Let G = (V (G), E(G)) be a finite simple graph without loops. The neighbourhood N (v) of a vertex v is the set of vertices adjacent to v. The degree d(v) of v is |N (v)|. The minimum and maximum degree of G are denoted by δ(G) and 1(G), respectively. For a vertex v ∈ V (G) and a subset S ⊆ V (G), NS(v) is the set of neighbours of v contained in S, i.e.,… (More)
In this paper, we obtain some new results R(5, 12) 848, R(5, 14) 1461, etc., and we obtain new upper bound formulas for Ramsey numbers with parameters. © 2006 Published by Elsevier B.V.
For two given graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest positive integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. Let Sn denote a star of order n and Wm a wheel of order m+1. This paper shows that R(Sn, W6) = 2n+1 for n ≥ 3 and R(Sn, Wm ) = 3n − 2 for m odd and n ≥ m − 1 ≥ 2. © 2003… (More)