The k-Ramsey number of two five cycles
AbstractGiven any two graphs F and H, the Ramsey number R(F, H) is defined as the smallest positive integer n such that every red-blue coloring of the edges of the complete graph Kn of order n, there will be a subgraph of Kn isomorphic to F whose edges are all colored red (a red F) or a subgraph of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2023.2250839 |
| Summary: | AbstractGiven any two graphs F and H, the Ramsey number R(F, H) is defined as the smallest positive integer n such that every red-blue coloring of the edges of the complete graph Kn of order n, there will be a subgraph of Kn isomorphic to F whose edges are all colored red (a red F) or a subgraph of Kn isomorphic to H whose edges are all colored blue (a blue H). If F and H are bipartite graphs, then the k-Ramsey number [Formula: see text] is defined as the smallest positive integer n such that for any red-blue coloring of the edges of the complete k-partite graph of order n in which each partite set is of order [Formula: see text] or [Formula: see text] there will be a subgraph isomorphic to F whose edges are all colored red (a red F) or a subgraph isomorphic to H whose edges are all colored blue (a blue H). Andrews, Chartrand, Lumduanhom and Zhang found the k-Ramsey number [Formula: see text] for [Formula: see text], and for [Formula: see text] and [Formula: see text] where [Formula: see text]. We continue their work by investigating the case where the graphs F and H are both C5. |
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| ISSN: | 0972-8600 2543-3474 |