Multipartite Ramsey numbers of complete bipartite graphs arising from algebraic combinatorial structures
Combinatorics
2023-07-20 v1
Abstract
In 2019, Perondi and Carmelo determined the set multipartite Ramsey number of particular complete bipartite graphs by establishing a relationship between the set multipartite Ramsey number, Hadamard matrices, and strongly regular graphs, which is a breakthrough in Ramsey theory. However, since Hadamard matrices of order not divisible by 4 do not exist, many open problems have arisen. In this paper, we generalize Perondi and Carmelo's results by introducing the -Hadamard matrix that we conjecture exists for arbitrary order. Finally, we determine set and size multipartite Ramsey numbers for particular complete bipartite graphs.
Keywords
Cite
@article{arxiv.2307.09736,
title = {Multipartite Ramsey numbers of complete bipartite graphs arising from algebraic combinatorial structures},
author = {I Wayan Palton Anuwiksa and Rinovia Simanjuntak and Edy Tri Baskoro},
journal= {arXiv preprint arXiv:2307.09736},
year = {2023}
}
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15 pages