A characterization on $(g,f)$-parity orientations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913304684789760 |
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| author | Lu, Hongliang Ma, Xinxin |
| author_facet | Lu, Hongliang Ma, Xinxin |
| contents | Let $G$ be a graph and $g,f:V(G)\to2^N$ be two set functions such that $g(v)\le f(v)$ and $g(v)\equiv f(v)\pmod 2$ for every $v\in V(G)$. An orientation $O$ of $G$ is called a $(g,f)$-parity orientation if $g(v)\le d^+_O(v)\le f(v)$ and $g(v)\equiv d^+_O(v)\pmod 2$ for every $v\in V(G)$. In this paper, we give a Tutte-type characterization for a graph to have a $(g,f)$-parity orientation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04797 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization on $(g,f)$-parity orientations Lu, Hongliang Ma, Xinxin Combinatorics Let $G$ be a graph and $g,f:V(G)\to2^N$ be two set functions such that $g(v)\le f(v)$ and $g(v)\equiv f(v)\pmod 2$ for every $v\in V(G)$. An orientation $O$ of $G$ is called a $(g,f)$-parity orientation if $g(v)\le d^+_O(v)\le f(v)$ and $g(v)\equiv d^+_O(v)\pmod 2$ for every $v\in V(G)$. In this paper, we give a Tutte-type characterization for a graph to have a $(g,f)$-parity orientation. |
| title | A characterization on $(g,f)$-parity orientations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.04797 |