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- W2801430724 abstract "A graph $H=(W,E_H)$ is said to have bandwidth at most $b$ if there exists a labeling of $W$ as $w_1,w_2,dots,w_n$ such that $|i-j|leq b$ for every edge $w_iw_jin E_H$, and a bipartite balanced $(beta,Delta)$-graph $H$ is a bipartite graph with bandwidth at most $beta |W|$ and maximum degree at most $Delta$, and furthermore it has a proper 2-coloring $chi :Wrightarrow[2]$ such that $||chi^{-1}(1)|-|chi^{-1}(2)||leqbeta|chi^{-1}(2)|$. We prove that for any fixed $0<gamma<1$ and integer $Deltage1$, there exist a constant $beta=beta(gamma,Delta)>0$ and a natural number $n_0$ such that for every balanced $(beta,Delta)$-graph $H$ on $ngeq n_0$ vertices the bipartite Ramsey number $br(H,H)$ is at most $(1+gamma)n$. In particular, $br(C_{2n},C_{2n})=(2+o(1))n$." @default.
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- W2801430724 date "2018-04-27" @default.
- W2801430724 modified "2023-10-18" @default.
- W2801430724 title "Bipartite Ramsey Numbers for Graphs of Small Bandwidth" @default.
- W2801430724 doi "https://doi.org/10.37236/7334" @default.
- W2801430724 hasPublicationYear "2018" @default.
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