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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
Eigenvalues and triangles in graphs
TLDR
It is proved that every non-bipartite graph of order and size contains a triangle if one of the following is true: $(G) \ge \sqrt {m - 1} $ and $G \ne {C_5} \cup (n - 5){K_1}$.
Wiener index, Harary index and Hamiltonicity of graphs
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
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
Color Degree Sum Conditions for Rainbow Triangles in Edge-Colored Graphs
TLDR
This paper proves that an edge-colored graph on n vertices contains a rainbow triangle if the color degree sum of every two adjacent vertices is at least $$n-1$$n+1.
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