Antidirected subgraphs of oriented graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910298580975616 |
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| author | Stein, Maya Zárate-Guerén, Camila |
| author_facet | Stein, Maya Zárate-Guerén, Camila |
| contents | We show that for every $η>0$ every sufficiently large $n$-vertex oriented graph D of minimum semidegree exceeding $(1 + η) k/2$ contains every balanced antidirected tree with $k$ edges and bounded maximum degree, if $k \ge ηn$. In particular, this asymptotically confirms a conjecture of the first author for long antidirected paths and dense digraphs.
Further, we show that in the same setting, D contains every $k$-edge antidirected subdivision of a sufficiently small complete graph, if the paths of the subdivision that have length 1 or 2 span a forest. As a special case, we can find all antidirected cycles of length at most $k$.
Finally, we address a conjecture of Addario-Berry, Havet, Linhares Sales, Reed and Thomassé for antidirected trees in digraphs. We show that this conjecture is asymptotically true in $n$-vertex oriented graphs for all balanced antidirected trees of bounded maximum degree and of size linear in $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00769 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Antidirected subgraphs of oriented graphs Stein, Maya Zárate-Guerén, Camila Combinatorics We show that for every $η>0$ every sufficiently large $n$-vertex oriented graph D of minimum semidegree exceeding $(1 + η) k/2$ contains every balanced antidirected tree with $k$ edges and bounded maximum degree, if $k \ge ηn$. In particular, this asymptotically confirms a conjecture of the first author for long antidirected paths and dense digraphs. Further, we show that in the same setting, D contains every $k$-edge antidirected subdivision of a sufficiently small complete graph, if the paths of the subdivision that have length 1 or 2 span a forest. As a special case, we can find all antidirected cycles of length at most $k$. Finally, we address a conjecture of Addario-Berry, Havet, Linhares Sales, Reed and Thomassé for antidirected trees in digraphs. We show that this conjecture is asymptotically true in $n$-vertex oriented graphs for all balanced antidirected trees of bounded maximum degree and of size linear in $n$. |
| title | Antidirected subgraphs of oriented graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2212.00769 |