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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Vydáno v:Graphs and combinatorics Ročník 41; číslo 6; s. 116
Hlavní autoři: Ai, Lianyang, Zhang, Wenqian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Tokyo Springer Japan 01.12.2025
Springer Nature B.V
Témata:
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
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Popis
Shrnutí: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 ].
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-025-02980-z