Eigenvalues and parity factors in graphs with given minimum degree

Let G be a graph and let g,f be nonnegative integer-valued functions defined on V(G) such that g(v)≤f(v) and g(v)≡f(v)(mod2) for all v∈V(G). A (g,f)-parity factor of G is a spanning subgraph H such that for each vertex v∈V(G), g(v)≤dH(v)≤f(v) and f(v)≡dH(v)(mod2). We prove sharp upper bounds for cer...

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Bibliographic Details
Published in:Discrete mathematics 2023-04, Vol.346 (4), p.113290, Article 113290
Main Authors: Kim, Donggyu, O, Suil
Format: Article
Language:English
Subjects:
[formula omitted]-Factors
Eigenvalues
Parity factors
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Summary:Let G be a graph and let g,f be nonnegative integer-valued functions defined on V(G) such that g(v)≤f(v) and g(v)≡f(v)(mod2) for all v∈V(G). A (g,f)-parity factor of G is a spanning subgraph H such that for each vertex v∈V(G), g(v)≤dH(v)≤f(v) and f(v)≡dH(v)(mod2). We prove sharp upper bounds for certain eigenvalues in an h-edge-connected graph G with given minimum degree to guarantee the existence of a (g,f)-parity factor.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2022.113290