{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:55:12Z","timestamp":1787324112428,"version":"build-2736575974"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100012468","name":"Distinguished Young Scientific Research Talents Plan in Universities of Fujian Province","doi-asserted-by":"publisher","award":["SJ2017-29"],"award-info":[{"award-number":["SJ2017-29"]}],"id":[{"id":"10.13039\/501100012468","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671088"],"award-info":[{"award-number":["11671088"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>The notion of goodness for Ramsey numbers was introduced by Burr and Erd\u00f6s in 1983. For graphs $G$ and $H$, let $G+H$ be the graph obtained from disjoint $G$ and $H$ by adding all edges between the vertices of $G$ and $H$. Denote $nH$ by the union of $n$ disjoint copies of $H$. Let $B_n^{(k)}=K_k+nK_1$, which is called a book. We first obtain that if $t\\ge1$ and $k\\ge2$ are fixed integers and $G$ is a fixed graph, then for all large $n$, $r(K_{1,t}+G, B_n^{(k)})\\le (\\chi(G)+1)(n+kt-1)+1.$ This is sharp for several classes of graphs. Faudree, Rousseau, and Sheehan in 1978 proved that $q^2+q+2\\le r(C_4,B_{q^2-q+1}^{(2)})\\le q^2+q+4$ for prime power $q$, which implies that $B_n^{(2)}$ is not $C_4$-good for $q^2-q+1\\le n\\le q^2+q$. It is very difficult to determine the exact values for $r(C_4,B_{n}^{(2)})$. Moreover, Nikiforov and Rousseau in 2009 already proved that $B_n^{(k)}$ is $(K_2+C_4)$-good for fixed $k\\ge 2$ and large $n$. In this paper, we obtain that for fixed $k\\ge 2$ and large $n$, \\scriptsize$ r(K_1+C_4, B_n^{(k)}) = \\left\\{ \\begin{array}{ll} 2(n+2k-1) {if $n$ is even,}\\\\ 2(n+2k-1)+1 {if $n$ is odd.} \\end{array} \\right. $ This implies that $B_n^{(k)}$ is not $(K_1+C_4)$-good for each fixed $k\\ge2$.<\/jats:p>","DOI":"10.1137\/20m1365867","type":"journal-article","created":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T10:12:34Z","timestamp":1609841554000},"page":"23-34","source":"Crossref","is-referenced-by-count":8,"title":["Ramsey Numbers Involving Large Books"],"prefix":"10.1137","volume":"35","author":[{"given":"Qizhong","family":"Lin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiudi","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,1,5]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"B. Bollob\u00e1s,\n                      Modern Graph Theory\n                      , Springer, New York, 1998.","DOI":"10.1007\/978-1-4612-0619-4"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-24.3.405"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070106"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070404"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010118"},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"D. Conlon,\n                      The Ramsey number of books\n                      , Adv. Combin., 3 (2019), 12pp.","DOI":"10.19086\/aic.10808"},{"key":"atypb7","unstructured":"D. Conlon, J. Fox, and Y. Wigderson,\n                      Ramsey Numbers of Books and Quasirandomness\n                      , preprint,arXiv:2001.00407."},{"key":"atypb8","first-page":"459","volume":"7","author":"Erd\u00f6s P.","year":"1962","journal-title":"Magyar Tud. Akad. Mat. Kutat\u00f3 Int. K\u00f6zl."},{"key":"atypb9","first-page":"117","author":"Erd\u00f6s P.","year":"1966","journal-title":"New York"},{"key":"atypb10","unstructured":"P. Erd\u00f6s,\n                      On Some New Inequalities Concerning Extremal Properties of Graphs\n                      , Theory of Graph, Proc. Colloy, Tihany, vol. 1966, P. Erd\u00f6s and G. Katona, eds., Academic Press, New York, 1968, pp. 77-81."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02018930"},{"key":"atypb12","first-page":"111","volume":"1","author":"Erd\u00f6s P.","year":"1988","journal-title":"Series A: Mathematical Sciences"},{"key":"atypb13","unstructured":"P. Erd\u00f6s and M. Simonovits,\n                      A limit theorem in graph theory\n                      , Scientia, Series A: Math. Sci. (1988), pp. 51-57."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1946-08715-7"},{"key":"atypb15","first-page":"289","author":"Faudree R. J.","year":"1978","journal-title":"Winnipeg"},{"key":"atypb16","first-page":"239","volume":"31","author":"Faudree R. J.","year":"1991","journal-title":"Ars Combin."},{"key":"atypb17","first-page":"351","author":"Faudree R. J.","year":"1981","journal-title":"New York"},{"key":"atypb18","unstructured":"J. Koml\u00f3s and M. Simonovits,\n                      Szemer\u00e9di's regularity lemma and its applications in graph theory\n                      , Combinatorics, Paul Erd\u00f6s is Eighty, Vol. 2 (Keszthely,1993), Bolyai Soc. Math. Stud, vol. 2, J\u00e1nos Bolyai Math. Soc. Budapest, (1996), pp. 295-352."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01196135"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199612)23:4<413::AID-JGT10>3.0.CO;2-D"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2009.10.011"},{"key":"atypb22","unstructured":"Q. Lin and X. Peng,\n                      Large Book-cycle Ramsey Numbers\n                      , preprint,arXiv:1909.13533v2."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2016.04.012"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2004.03.009"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20071"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20081"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548305006929"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-009-2409-2"},{"key":"atypb29","unstructured":"S. Radziszowski,\n                      Small Ramsey numbers\n                      , Electron. J. Combin. (2017), DS1."},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190020110"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-18.3.392"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2009.07.004"},{"key":"atypb33","first-page":"279","author":"Simonovits M.","year":"1968","journal-title":"New York"},{"key":"atypb34","unstructured":"E. Szemer\u00e9di,\n                      Regular partitions of graphs\n                      , Probl\u00e9mes Combinatories et th\u00e9orie des graphs, Colloque Inter. CNRS, Univ. Orsay, Orsay, 1976, J. Bermond, J. Fournier, M. Las Vergnas, and D. Scotteau, eds., 1978, pp. 399-402."},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(82)80038-3"},{"key":"atypb36","first-page":"436","volume":"48","author":"Tur\u00e1n P.","year":"1941","journal-title":"Math Fiz. Lapok"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00049-2"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1365867","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:18:49Z","timestamp":1787321929000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1365867"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1365867"],"URL":"https:\/\/doi.org\/10.1137\/20m1365867","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}