Characterization of graphs without even $F$-orientations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2015
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| _version_ | 1866916164330848256 |
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| author | Abreu, M. Labbate, D. Romaniello, F. Sheehan, J. |
| author_facet | Abreu, M. Labbate, D. Romaniello, F. Sheehan, J. |
| contents | A graph $G$ is $1$-extendible if every edge belongs to at least one $1$-factor of $G$. Let $G$ be a graph with a $1$-factor $F$. Then an even $F$-orientation of $G$ is an orientation in which each $F$-alternating cycle has exactly an even number of edges directed in the same fixed direction around the cycle. In this paper, we examine the structure of 1-extendible graphs $G$ which have no even $F$-orientation where $F$ is a fixed $1$-factor of $G$. In the case of graphs of connectivity at least four and k-regular graphs for $k \geq 3$ we give a complete characterization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1501_02437 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Characterization of graphs without even $F$-orientations Abreu, M. Labbate, D. Romaniello, F. Sheehan, J. Combinatorics A graph $G$ is $1$-extendible if every edge belongs to at least one $1$-factor of $G$. Let $G$ be a graph with a $1$-factor $F$. Then an even $F$-orientation of $G$ is an orientation in which each $F$-alternating cycle has exactly an even number of edges directed in the same fixed direction around the cycle. In this paper, we examine the structure of 1-extendible graphs $G$ which have no even $F$-orientation where $F$ is a fixed $1$-factor of $G$. In the case of graphs of connectivity at least four and k-regular graphs for $k \geq 3$ we give a complete characterization. |
| title | Characterization of graphs without even $F$-orientations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1501.02437 |