{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T09:14:41Z","timestamp":1766049281919,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A graph $H=(W,E_H)$ is said to have bandwidth\u00a0at 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 $w_iw_j\\in E_H$, and a bipartite balanced $(\\beta,\\Delta)$-graph\u00a0$H$ is a bipartite graph with bandwidth at most $\\beta |W|$ and maximum degree at most $\\Delta$, and furthermore it has a proper 2-coloring $\\chi :W\\rightarrow[2]$ such that $||\\chi^{-1}(1)|-|\\chi^{-1}(2)||\\leq\\beta|\\chi^{-1}(2)|$. We prove that for any fixed $0&lt;\\gamma&lt;1$ and integer $\\Delta\\ge1$, there exist a constant $\\beta=\\beta(\\gamma,\\Delta)&gt;0$ and a natural number $n_0$ such that for every balanced $(\\beta,\\Delta)$-graph $H$ on $n\\geq n_0$ vertices the bipartite Ramsey number $br(H,H)$ is at most $(1+\\gamma)n$. In particular, $br(C_{2n},C_{2n})=(2+o(1))n$.<\/jats:p>","DOI":"10.37236\/7334","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:33:59Z","timestamp":1578670439000},"source":"Crossref","is-referenced-by-count":7,"title":["Bipartite Ramsey Numbers for Graphs of Small Bandwidth"],"prefix":"10.37236","volume":"25","author":[{"given":"Lili","family":"Shen","sequence":"first","affiliation":[]},{"given":"Qizhong","family":"Lin","sequence":"additional","affiliation":[]},{"given":"Qinghai","family":"Liu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,4,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:34:19Z","timestamp":1579235659000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,27]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7334","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,4,27]]},"article-number":"P2.16"}}