Sufficient conditions for a graph with minimum degree to be k-critical with respect to [1,b]-odd factor
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913686217555968 |
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| author | Zhou, Sizhong |
| author_facet | Zhou, Sizhong |
| contents | A spanning subgraph $F$ of a graph $G$ is called a $[1,b]$-odd factor if $b\equiv1$ (mod 2) and $d_F(v)\in\{1,3,\ldots,b\}$ for every $v\in V(G)$. A graph $G$ of order $n\geq k+2$ is $k$-critical with respect to $[1,b]$-odd factor if for any $X\subseteq V(G)$ with $|X|=k$, $G-X$ has a $[1,b]$-odd factor. In this paper, we provide a size and spectral radius conditions for a graph with minimum degree to be $k$-critical with respect to $[1,b]$-odd factor, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sufficient conditions for a graph with minimum degree to be k-critical with respect to [1,b]-odd factor Zhou, Sizhong Combinatorics 05C50, 05C70 A spanning subgraph $F$ of a graph $G$ is called a $[1,b]$-odd factor if $b\equiv1$ (mod 2) and $d_F(v)\in\{1,3,\ldots,b\}$ for every $v\in V(G)$. A graph $G$ of order $n\geq k+2$ is $k$-critical with respect to $[1,b]$-odd factor if for any $X\subseteq V(G)$ with $|X|=k$, $G-X$ has a $[1,b]$-odd factor. In this paper, we provide a size and spectral radius conditions for a graph with minimum degree to be $k$-critical with respect to $[1,b]$-odd factor, respectively. |
| title | Sufficient conditions for a graph with minimum degree to be k-critical with respect to [1,b]-odd factor |
| topic | Combinatorics 05C50, 05C70 |
| url | https://arxiv.org/abs/2502.07519 |