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Spectral analogues of Erdős’ and Moon–Moser’s theorems on Hamilton cycles
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
The formula for Turán number of spanning linear forests
TLDR
Wiener index, Harary index and Hamiltonicity of graphs
- Hongbo Hua, Bo Ning
- Mathematics
- 1 September 2016
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
On sufficient conditions for rainbow cycles in edge-colored graphs
TLDR
Stability Results on the Circumference of a Graph
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Rainbow triangles in edge-colored graphs
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Ore- and Fan-type heavy subgraphs for Hamiltonicity of 2-connected graphs
TLDR
Spectral radius and Hamiltonian properties of graphs
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
Spectral analogues of Moon–Moser's theorem on Hamilton paths in bipartite graphs
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
Spectral radius and traceability of connected claw-free graphs
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
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