Geodesic
Partitioning planar graph of girth 5 into two forests with maximum degree 4
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 355-366 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Given a graph $G=(V, E)$, if we can partition the vertex set $V$ into two nonempty subsets $V_1$ and $V_2$ which satisfy $\Delta (G[V_1])\le d_1$ and $\Delta (G[V_2])\le d_2$, then we say $G$ has a $(\Delta _{d_{1}},\Delta _{d_{2}})$-partition. And we say $G$ admits an $(F_{d_{1}}, F_{d_{2}})$-partition if $G[V_1]$ and $G[V_2]$ are both forests whose maximum degree is at most $d_{1}$ and $d_{2}$, respectively. We show that every planar graph with girth at least 5 has an $(F_4, F_4)$-partition.
Given a graph $G=(V, E)$, if we can partition the vertex set $V$ into two nonempty subsets $V_1$ and $V_2$ which satisfy $\Delta (G[V_1])\le d_1$ and $\Delta (G[V_2])\le d_2$, then we say $G$ has a $(\Delta _{d_{1}},\Delta _{d_{2}})$-partition. And we say $G$ admits an $(F_{d_{1}}, F_{d_{2}})$-partition if $G[V_1]$ and $G[V_2]$ are both forests whose maximum degree is at most $d_{1}$ and $d_{2}$, respectively. We show that every planar graph with girth at least 5 has an $(F_4, F_4)$-partition.
DOI : 10.21136/CMJ.2024.0394-21
Classification : 05C10, 05C69
Keywords: vertex partition; girth; forest; maximum degree 
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     title = {Partitioning planar graph of girth 5 into two forests with maximum degree 4},
     journal = {Czechoslovak Mathematical Journal},
     pages = {355--366},
     year = {2024},
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     doi = {10.21136/CMJ.2024.0394-21},
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Chen, Min; Raspaud, André; Wang, Weifan; Yu, Weiqiang. Partitioning planar graph of girth 5 into two forests with maximum degree 4. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 355-366. doi: 10.21136/CMJ.2024.0394-21

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