Learn More
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 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)
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)