A spectral condition for Hamilton cycles in tough bipartite graphs

Let G be a graph. The spectral radius of G is the largest eigenvalue of its adjacency matrix. For a non-complete bipartite graph G with parts X and Y , the bipartite toughness of G is defined as t B ( G ) = min | S | c ( G - S ) , where the minimum is taken over all proper subsets S ⊂ X (or S ⊂ Y )...

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Bibliographic Details
Published in:Graphs and combinatorics Vol. 41; no. 6; p. 116
Main Authors: Ai, Lianyang, Zhang, Wenqian
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.12.2025
Springer Nature B.V
Subjects:
Combinatorics
Eigenvalues
Engineering Design
Equality
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Original Paper
 
05C50
Spectral radius
Hamilton cycle
Bipartite graph
[
factor
ISSN:0911-0119, 1435-5914
Online Access:Get full text
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Summary:Let G be a graph. The spectral radius of G is the largest eigenvalue of its adjacency matrix. For a non-complete bipartite graph G with parts X and Y , the bipartite toughness of G is defined as t B ( G ) = min | S | c ( G - S ) , where the minimum is taken over all proper subsets S ⊂ X (or S ⊂ Y ) such that c ( G - S ) > 1 . In this paper, we give a sharp spectral radius condition for balanced bipartite graphs G with t B ( G ) ≥ 1 to guarantee that G contains Hamilton cycles. This solves a problem proposed in [ 9 ].
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content type line 14
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-025-02980-z