An in-tournament is an oriented graph such that the in-neighborhood of every vertex induces a tournament. Therefore, in-tournaments are a generalization of local tournaments where, for every vertex, the set of inneighbors as well as the set of out-neighbors induce a tournament. While local tournaments have been intensively studied very little is known about in-tournaments. It is the purpose of ...

Asratian and Khachatrian proved that a connected graph G of order at least 3 is hamiltonian if d(u) + d(v);;::: JN(u) U N(v) U N.(w)I for any path uwv with uv ff E(G), .where N(x) is the neighborhood of a vertex x. We prove that a graph G with this condition, which is not complete bipartite, has the following properties: a) For each pair of vertices x, y with distance d(x, y) 2:: 3 and for each...

A graph G is said to be pancyclic if it contains cycles of all lengths from 4 to |V (G)| in G. For any two vertices u, v ∈ V (G), a cycle is called a geodesic cycle with u and v if a shortest path joining u and v lies on the cycle. Let G be a bipartite graph. For any two vertices u and v in G, a cycle C is called a balanced cycle between u and v if dC(u, v) = max{dC(x, y) | dG(x, u) and dG(y, v...

LetH be a multigraph, possibly containing loops. AnH-subdivision is any simple graph obtained by replacing the edges of H with paths of arbitrary length. Let H be an arbitrary multigraph of order k, size m, n0(H) isolated vertices and n1(H) vertices of degree one. In [10] it was shown that if G is a simple graph of order n containing an H-subdivision H and δ(G) ≥ n+m−k+n1(H)+2n0(H) 2 , then G c...

with Local Ore-Type Conditions II A.S. Asratian, R H aggkvist and G.V. Sarkisian University of Ume a January, 1994 Abstract. It is well known due Ore that a graph G of order at least 3 is Hamiltonconnected if d(u) + d(v) jV (G)j + 1 for each pair of nonadjacent vertices u and v. We consider here connected graphs G of order at least 3 where d(u) + d(v) jN(u) [N(v) [N(w)j+ 1 for each triple of v...

Let D be a semicomplete multipartite digraph, with partite sets (called color classes) V 1 ; V 2 ; : : :; V c , such that jV 1 j jV 2 j : : : jV c j. Deene f(D) = jV (D)j ? 3jV c j + 1 and g(D) = jV (D)j?jVc?1j?2jVcj+2 2. We deene the irregularity i(D) of D to be maxjd + (x) ? d ? (y)j over all vertices x and y of D (possibly x = y). We deene the local irregularity i l (D) of D to be maxjd + (x...

Jwo et al. [Networks 23 (1993) 315–326] introduced the alternating group graph as an interconnection network topology for computing systems. They showed that the proposed structure has many advantages over n-cubes and star graphs. For example, all alternating group graphs are hamiltonian-connected (i.e., every pair of vertices in the graph are connected by a hamiltonian path) and pancyclic (i.e...

A. S. Asratian DEPARTMENT OF MATHEMATICS UNIVERSITY OF UMEA S-907 87, UMEA, SWEDEN DEPARTMENT OF MATHEMATICAL CYBERNETICS YEREVAN STATE UNIVERSITY YEREVAN, 375049, REPUBLIC OF ARMENIA R. Haggkvist DEPARTMENT OF MATHEMATICS UNIVERSITY OF UMEA S-907 87, UMEA, SWEDEN G. V. Sarkisian DEPARTMENT OF MATHEMATICAL CYBERNETICS YEREVAN STATE UNIVERSITY YEREVAN, 375049, REPUBLIC OF ARMENIA It is well know...

For positive integers n and q and a monotone graph property A, we consider the two player, perfect information game WC(n, q,A), which is defined as follows. The game proceeds in rounds. In each round, the first player, called Waiter, offers the second player, called Client, q + 1 edges of the complete graph Kn which have not been offered previously. Client then chooses one of these edges which ...

A digraph of order at least k is termed k-traceable if each of its subdigraphs of order k is traceable. It turns out that several properties of tournaments—i.e., the 2-traceable oriented graphs—extend to k-traceable oriented graphs for small values of k. For instance, the authors together with O. Oellermann have recently shown that for k = 2, 3, 4, 5, 6, all ktraceable oriented graphs are trace...