Spectral radius and Hamiltonian properties of graphs
74 citations recorded by the source corpus.
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 graph on vertices with . If , then contains a Hamilton path unless .(2) Let be a graph on vertices with . If , then contains a Hamilton cycle unless . As corollaries of our first result, two previous theorems due to Fiedler and Nikiforov and Lu et al. are obtained, respectively. Our second result refines another previous theorem of Fiedler and Nikiforov.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/cf5d93bbfeecb8813308389d15a27557717eb243
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Spectral radius and Hamiltonicity of graphs with large minimum degree (2016, background): “It should be noted that most of the results discussed in the present paper and in the references [1, 10, 13, 14, 15, 16, 17, 21] deal exclusively with very dense graphs, which makes these results somewhat one-sided.”
- Spectral analogues of Erdős’ and Moon–Moser’s theorems on Hamilton cycles (2015, background): “4, there are also some other works related to Problem 1, see [19, 20, 24].”
- Sufficient spectral conditions on Hamiltonian and traceable graphs (2014, unknown): “See [11] for a stronger result.”
- A survey on spectral conditions for some extremal graph problems (2021, background): “In 2015, Ning and Ge [160] refined the extremal result of Ore and the spectral result of Fiedler and Nikiforov for graphs with minimum degree at least two.”