Hamiltonicity in balancedk-partite graphs

One of the earliest results about hamiltonian graphs was given by Dirac. He showed that if a graphG has orderp and minimum degree at least thenG is hamiltonian. Moon and Moser showed that a balanced bipartite graph (the two partite sets have the same order)G has orderp and minimum degree more than thenG is hamiltonian. In this paper, their idea is generalized tok-partite graphs and the following result is obtained: LetG be a balancedk-partite graph with orderp = kn. If the minimum degree

Endpoint extendable paths in tournaments

Let s(n) be the threshold for which each directed path of order smaller than s(n) is extendible from one of its endpoints in some tournament T_n It is shown that s(n) is asymptotic to 3n/4, with an error term at most 3 for infinitely many n. There are six tournaments with s(n) = n. © 1996 John Wiley & Sons, Inc.     

All triangle-graph ramsey numbers for connected graphs of order six

The Ramsey numbers r(K_3′ G) are determined for all connected graphs G of order six.     

Size Ramsey numbers for small-order graphs

A table of the size Ramsey number or the restricted size Ramsey number for all pairs of graphs with at most four vertices and no isolated vertices is given.     

On k‐ordered graphs

Ng and Schultz [J Graph Theory 1 ( 6 ), 45–57] introduced the idea of cycle orderability. For a positive integer k, a graph G is k‐ordered if for every ordered sequence of k vertices, there is a cycle that encounters the vertices of the sequence in the given order. If the cycle is also a Hamiltonian cycle, then G is said to be k‐ordered Hamiltonian. We give sum of degree conditions for nonadjacent vertices and neighborhood union conditions that imply a graph is k‐ordered Hamiltonian. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 69–82, 2000