In 1962, Erdős gave a sufficient condition for Hamilton cycles in terms of the vertex number, edge number and minimum degree of graphs which generalized Ore’s theorem. One year later, Moon and Moser… Expand

In this paper, we prove tight sufficient conditions for traceability and Hamiltonicity of connected graphs with given minimum degree, in terms of Wiener index and Harary index. We also prove some… Expand

We give some sufficient conditions for the existence of rainbow triangles in edge-colored graphs in terms of color degree, color number and edge number.Expand

We characterize all pairs of forbidden subgraphs that imply a 2-connected graph to be Hamiltonian by restricting Ore- and Fan-type degree conditions.Expand

Let be a graph with minimum degree . The spectral radius of , denoted by , is the largest eigenvalue of the adjacency matrix of . In this note, we mainly prove the following two results.(1) Let be a… Expand

Abstract In 1962, Erdős proved a theorem on the existence of Hamilton cycles in graphs with given minimum degree and number of edges. Significantly strengthening in case of balanced bipartite graphs,… Expand

Let $G$ be a connected claw-free graph on $n$ vertices and $\overline{G}$ be its complement graph. Let $\mu(G)$ be the spectral radius of $G$. Denote by $N_{n-3,3}$ the graph consisting of $K_{n-3}$… Expand