Separating paths systems of almost linear size
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914815069388800 |
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| author | Letzter, Shoham |
| author_facet | Letzter, Shoham |
| contents | A separating path system for a graph $G$ is a collection $\mathcal{P}$ of paths in $G$ such that for every two edges $e$ and $f$ in $G$, there is a path in $\mathcal{P}$ that contains $e$ but not $f$. We show that every $n$-vertex graph has a separating path system of size $O(n \log^* n)$. This improves upon the previous best upper bound of $O(n \log n)$, and makes progress towards a conjecture of Falgas-Ravry--Kittipassorn--Korándi--Letzter--Narayanan and Balogh--Csaba--Martin--Pluhár, according to which an $O(n)$ bound should hold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_07732 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Separating paths systems of almost linear size Letzter, Shoham Combinatorics A separating path system for a graph $G$ is a collection $\mathcal{P}$ of paths in $G$ such that for every two edges $e$ and $f$ in $G$, there is a path in $\mathcal{P}$ that contains $e$ but not $f$. We show that every $n$-vertex graph has a separating path system of size $O(n \log^* n)$. This improves upon the previous best upper bound of $O(n \log n)$, and makes progress towards a conjecture of Falgas-Ravry--Kittipassorn--Korándi--Letzter--Narayanan and Balogh--Csaba--Martin--Pluhár, according to which an $O(n)$ bound should hold. |
| title | Separating paths systems of almost linear size |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2211.07732 |