Hitting minors, subdivisions, and immersions in tournaments
The Erd\H{o}s-P\'osa property relates parameters of covering and packing of combinatorial structures and has been mostly studied in the setting of undirected graphs. In this note, we use results of Chudnovsky, Fradkin, Kim, and Seymour to show that, for every directed graph $H$ (resp. strongly-...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2018-01-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3139/pdf |
| _version_ | 1797270095124234240 |
|---|---|
| author | Jean-Florent Raymond |
| author_facet | Jean-Florent Raymond |
| author_sort | Jean-Florent Raymond |
| collection | DOAJ |
| description | The Erd\H{o}s-P\'osa property relates parameters of covering and packing of
combinatorial structures and has been mostly studied in the setting of
undirected graphs. In this note, we use results of Chudnovsky, Fradkin, Kim,
and Seymour to show that, for every directed graph $H$ (resp.
strongly-connected directed graph $H$), the class of directed graphs that
contain $H$ as a strong minor (resp. butterfly minor, topological minor) has
the vertex-Erd\H{o}s-P\'osa property in the class of tournaments. We also prove
that if $H$ is a strongly-connected directed graph, the class of directed
graphs containing $H$ as an immersion has the edge-Erd\H{o}s-P\'osa property in
the class of tournaments. |
| first_indexed | 2024-04-25T01:58:49Z |
| format | Article |
| id | doaj.art-b3c0554ec1b34c45b43839b60b2d1efe |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:58:49Z |
| publishDate | 2018-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-b3c0554ec1b34c45b43839b60b2d1efe2024-03-07T15:36:37ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502018-01-01Vol. 20 no. 1Graph Theory10.23638/DMTCS-20-1-53139Hitting minors, subdivisions, and immersions in tournamentsJean-Florent Raymondhttps://orcid.org/0000-0003-4646-7602The Erd\H{o}s-P\'osa property relates parameters of covering and packing of combinatorial structures and has been mostly studied in the setting of undirected graphs. In this note, we use results of Chudnovsky, Fradkin, Kim, and Seymour to show that, for every directed graph $H$ (resp. strongly-connected directed graph $H$), the class of directed graphs that contain $H$ as a strong minor (resp. butterfly minor, topological minor) has the vertex-Erd\H{o}s-P\'osa property in the class of tournaments. We also prove that if $H$ is a strongly-connected directed graph, the class of directed graphs containing $H$ as an immersion has the edge-Erd\H{o}s-P\'osa property in the class of tournaments.https://dmtcs.episciences.org/3139/pdfcomputer science - discrete mathematics05c70g.2.2 |
| spellingShingle | Jean-Florent Raymond Hitting minors, subdivisions, and immersions in tournaments Discrete Mathematics & Theoretical Computer Science computer science - discrete mathematics 05c70 g.2.2 |
| title | Hitting minors, subdivisions, and immersions in tournaments |
| title_full | Hitting minors, subdivisions, and immersions in tournaments |
| title_fullStr | Hitting minors, subdivisions, and immersions in tournaments |
| title_full_unstemmed | Hitting minors, subdivisions, and immersions in tournaments |
| title_short | Hitting minors, subdivisions, and immersions in tournaments |
| title_sort | hitting minors subdivisions and immersions in tournaments |
| topic | computer science - discrete mathematics 05c70 g.2.2 |
| url | https://dmtcs.episciences.org/3139/pdf |
| work_keys_str_mv | AT jeanflorentraymond hittingminorssubdivisionsandimmersionsintournaments |