Partition of Sparse Graphs into Two Forests with Bounded Degree
| Autor: | Yancey, Matthew |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Borodin and Kostochka proved that for $d_2 \geq 2d_1+2$ and a graph $G$ where every subgraph $H$ satisfies $$ e(H) < \left(2 - \frac{d_2+2}{(d_1+2)(d_2+1)}\right)n(H) + \frac{1}{d_2+1} $$ has a vertex partition $V(G) = V_1 \cup V_2$ such that $G[V_i]$ has maximum degree at most $d_i$ for each $i$. We show that under the same conditions we can additionally conclude that each $G[V_i]$ is a forest. |
| Databáze: | arXiv |
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