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引用次数: 0
摘要
摘要 我们证明，每一个路径宽度严格小于 a 的图，如果不包含 \(2^b\) 个顶点上的路径作为子图，那么它的树深度最多为 10ab。这个界限是在一个常数因子以内的最佳值。
Tight Bound on Treedepth in Terms of Pathwidth and Longest Path
Abstract
We show that every graph with pathwidth strictly less than a that contains no path on \(2^b\) vertices as a subgraph has treedepth at most 10ab. The bound is best possible up to a constant factor.
期刊介绍：
COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are
- Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups).
- Combinatorial optimization.
- Combinatorial aspects of geometry and number theory.
- Algorithms in combinatorics and related fields.
- Computational complexity theory.
- Randomization and explicit construction in combinatorics and algorithms.
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