Some results on the k-strong parity property in a graph
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915305939271680 |
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| author | Wu, Jie |
| author_facet | Wu, Jie |
| contents | A graph $G$ has the $k$-strong parity property if for any $X\subseteq V(G)$ with $|X|$ even, $G$ contains a spanning subgraph $F$ with $d_F(u)\equiv1$ (mod 2) for each $u\in X$ and $d_F(v)\in\{k,k+2,k+4,\ldots\}$ for each $v\in V(G)\setminus X$, where $k\geq2$ is an even integer. Kano and Matsumura proposed a characterization for a graph with the $k$-strong parity property (M. Kano, H. Matsumura, Odd-even factors of graphs, Graphs Combin. 41 (2025) 55). In this paper, we first give a size condition for a graph to have the $k$-strong parity property. Then we establish a signless Laplacian spectral radius condition to guarantee that a graph has the $k$-strong parity property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20352 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some results on the k-strong parity property in a graph Wu, Jie Combinatorics 05C50, 05C70, 90B99 A graph $G$ has the $k$-strong parity property if for any $X\subseteq V(G)$ with $|X|$ even, $G$ contains a spanning subgraph $F$ with $d_F(u)\equiv1$ (mod 2) for each $u\in X$ and $d_F(v)\in\{k,k+2,k+4,\ldots\}$ for each $v\in V(G)\setminus X$, where $k\geq2$ is an even integer. Kano and Matsumura proposed a characterization for a graph with the $k$-strong parity property (M. Kano, H. Matsumura, Odd-even factors of graphs, Graphs Combin. 41 (2025) 55). In this paper, we first give a size condition for a graph to have the $k$-strong parity property. Then we establish a signless Laplacian spectral radius condition to guarantee that a graph has the $k$-strong parity property. |
| title | Some results on the k-strong parity property in a graph |
| topic | Combinatorics 05C50, 05C70, 90B99 |
| url | https://arxiv.org/abs/2505.20352 |