On minimal k-factor-critical planar graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917073129570304 |
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| author | Li, Qiuli Lu, Fuliang Zhang, Heping |
| author_facet | Li, Qiuli Lu, Fuliang Zhang, Heping |
| contents | A graph of order $n$ is said to be \emph{$k$-factor-critical} ($0\leq k <n$) if the removal of any $k$ vertices results in a graph with a perfect matching.
A $k$-factor-critical graph $G$ is \emph{minimal} if $G-e$ is not $k$-factor-critical for any edge $e$ in $G$.
Favaron and Shi posed the conjecture that every minimal $k$-factor-critical graph is of minimum degree $k+1$ in 1998. In this paper, we confirm the conjecture for planar graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On minimal k-factor-critical planar graphs Li, Qiuli Lu, Fuliang Zhang, Heping Combinatorics A graph of order $n$ is said to be \emph{$k$-factor-critical} ($0\leq k <n$) if the removal of any $k$ vertices results in a graph with a perfect matching. A $k$-factor-critical graph $G$ is \emph{minimal} if $G-e$ is not $k$-factor-critical for any edge $e$ in $G$. Favaron and Shi posed the conjecture that every minimal $k$-factor-critical graph is of minimum degree $k+1$ in 1998. In this paper, we confirm the conjecture for planar graphs. |
| title | On minimal k-factor-critical planar graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.08137 |