Academic Journal
2-Reachable Subsets in Two-Colored Graphs
| Title: | 2-Reachable Subsets in Two-Colored Graphs |
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| Authors: | Gyárfás, András, Sárközy, Gábor N. |
| Publisher Information: | Springer |
| Publication Year: | 2026 |
| Collection: | MTAK: REAL (Library and Information Centre of the Hungarian Academy of Sciences / Magyar Tudományos Akadémia Könyvtár és Információs Központ) |
| Subject Terms: | QA166-QA166.245 Graphs theory / gráfelmélet |
| Description: | A subset X of vertices in a graph G is a diameter 2 subset if the distance of any two vertices of X is at most two in G[X] . Relaxing this notion, a subset X of vertices in a graph G is a 2-reachable subset if the distance of any two vertices of X is at most two in G . Related to recent attempts to strengthen a well-known conjecture of Ryser, English et al. conjectured that the vertices of a 2-edge-colored cocktail party graph (the graph obtained from a complete graph with an even number of vertices by deleting a perfect matching) can be covered by the vertices of two monochromatic diameter 2 subsets. In this note we prove the relaxed form of this conjecture, replacing diameter 2 by 2-reachable. An immediate corollary is that 2-colored cocktail party graphs on n vertices must contain a monochromatic 2-reachable subset with at least n\over 2 n 2 vertices (and this is best possible). |
| Document Type: | article in journal/newspaper |
| File Description: | text |
| Language: | English |
| ISSN: | 0911-0119 |
| Relation: | https://real.mtak.hu/237037/1/s00373-026-03036-6.pdf; Gyárfás, András and Sárközy, Gábor N. (2026) 2-Reachable Subsets in Two-Colored Graphs. GRAPHS AND COMBINATORICS, 42. ISSN 0911-0119 |
| DOI: | 10.1007/s00373-026-03036-6 |
| Availability: | https://real.mtak.hu/237037/ https://doi.org/10.1007/s00373-026-03036-6 |
| Rights: | cc_by |
| Accession Number: | edsbas.60159BDB |
| Database: | BASE |
| ISSN: | 09110119 |
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| DOI: | 10.1007/s00373-026-03036-6 |