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Currently displaying 1 – 9 of 9

Order by Relevance | Title | Year of publication

Degree powers in graphs with a forbidden even cycle.

Nikiforov, Vladimir — 2009

The Electronic Journal of Combinatorics [electronic only]

Revisiting two classical results on graph spectra.

Nikiforov, Vladimir — 2007

The Electronic Journal of Combinatorics [electronic only]

Linear combinations of graph eigenvalues.

Nikiforov, Vladimir — 2006

ELA. The Electronic Journal of Linear Algebra [electronic only]

Spectral saturation: inverting the spectral Turán theorem.

Nikiforov, Vladimir — 2009

The Electronic Journal of Combinatorics [electronic only]

The spectral radius of subgraphs of regular graphs.

Nikiforov, Vladimir — 2007

The Electronic Journal of Combinatorics [electronic only]

Graphs with many copies of a given subgraph.

Nikiforov, Vladimir — 2008

The Electronic Journal of Combinatorics [electronic only]

Degree powers in graphs with forbidden subgraphs.

Bollobás, Béla; Nikiforov, Vladimir — 2004

The Electronic Journal of Combinatorics [electronic only]

The sum of degrees in cliques.

Bollobás, Béla; Nikiforov, Vladimir — 2005

The Electronic Journal of Combinatorics [electronic only]

Spectral radius and Hamiltonicity of graphs with large minimum degree

Vladimir Nikiforov — 2016

Czechoslovak Mathematical Journal

Let $G$ be a graph of order $n$ and $λ (G)$ the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in $G$ . One of the main results of the paper is the following theorem: Let $k \geq 2,$ $n \geq k^{3} + k + 4,$ and let $G$ be a graph of order $n$ , with minimum degree $δ (G) \geq k .$ If $λ (G) \geq n - k - 1,$ then $G$ has a Hamiltonian cycle, unless $G = K_{1} \lor (K_{n - k - 1} + K_{k})$ or $G = K_{k} \lor (K_{n - 2 k} + {\bar{K}}_{k}) .$

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