A spectral condition for odd cycles in graphs

2007/07/30 by Vladimir Nikiforov, Nikiforov, Vladimir · 8 citations
Mathematics · #05C35 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Limits and Structures in Graph Theory #math.CO #msc:05C35 #msc:05C50

paper · pdf · doi:10.48550/arxiv.0707.4499

The main theorem is improved. Updated references

openalex publication_date 2007/07/30 · arxiv created 2007/11/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a sharp spectral condition for the existence of odd cycles in a graph of given order. We also prove a related stability result.

Cited by

• Nikiforov's spectral consecutive cycle problem and the connected-matching method
• Strong spectral stabilities for C_2k+1-free graphs
• Spectral extremal problem of the pth power of cycles
• Spectral extremal problems for non-bipartite graphs without odd cycles
• Some Turán-type results for signless Laplacian spectral radius
• Spectral extremal problem for the odd prism
• Spectral Turán problem of non-bipartite graphs: Forbidden books
• A Spectral Turán Problem for a Fixed Tree

Related

• Odd Properly Colored Cycles in Edge-Colored Graphs
• Disjoint type graphs with no short odd cycles
• Solution to a conjecture on the maximum skew-spectral radius of odd-cycle graphs
• Spectral conditions implying the existence of doubly chorded cycles without or with constraints
• The ratio of the numbers of odd and even cycles in outerplanar graphs