{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T14:52:39Z","timestamp":1778597559192,"version":"3.51.4"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,8,11]],"date-time":"2021-08-11T00:00:00Z","timestamp":1628640000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,11]],"date-time":"2021-08-11T00:00:00Z","timestamp":1628640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11901243"],"award-info":[{"award-number":["11901243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LQ19A010005"],"award-info":[{"award-number":["LQ19A010005"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LY18A010014"],"award-info":[{"award-number":["LY18A010014"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s10878-021-00791-5","type":"journal-article","created":{"date-parts":[[2021,8,11]],"date-time":"2021-08-11T20:02:33Z","timestamp":1628712153000},"page":"2748-2761","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal frequency assignment and planar list L(2,\u00a01)-labeling"],"prefix":"10.1007","volume":"44","author":[{"given":"Haiyang","family":"Zhu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1561-5772","authenticated-orcid":false,"given":"Junlei","family":"Zhu","sequence":"additional","affiliation":[]},{"given":"Ying","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Shuling","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Danjun","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Lianying","family":"Miao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,11]]},"reference":[{"key":"791_CR1","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1017\/S0963548398003411","volume":"8","author":"N Alon","year":"1999","unstructured":"Alon N (1999) Combinatorial nullstellensatz. Comb Probab Comput 8:7\u201329","journal-title":"Comb Probab Comput"},{"key":"791_CR2","doi-asserted-by":"publisher","first-page":"2201","DOI":"10.1016\/j.ejc.2007.04.019","volume":"28","author":"P Bella","year":"2007","unstructured":"Bella P, Kr\u00e1l D, Mohar B, Quittnerov\u00e1 K (2007) Labeling planar graphs with a condition at distance two. Eur J Comb 28:2201\u20132239","journal-title":"Eur J Comb"},{"key":"791_CR3","unstructured":"Borodin O, Broersma HJ, Glebov A, van den Heuvel J (2002) Stars and bunches in planar graphs. Part II: general planar graphs and colourings, CDAM research report series 2002\u201305"},{"key":"791_CR4","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1137\/S0895480193245339","volume":"9","author":"GJ Chang","year":"1996","unstructured":"Chang GJ, Kuo D (1996) The $$L(2,1)$$-labeling problem on graphs. SIAM J Disc Math 9:309\u2013316","journal-title":"SIAM J Disc Math"},{"key":"791_CR5","doi-asserted-by":"crossref","unstructured":"Dvo\u0159\u00e1k Z, Kr\u00e1l D, Nejedl\u00fd P, \u0160krekovski R (2008) Coloring squares of planar graphs with girth six. European J. Combin. 29 (4): 838\u2013849.","DOI":"10.1016\/j.ejc.2007.11.005"},{"key":"791_CR6","doi-asserted-by":"crossref","unstructured":"Fiala J, \u0160krekovski R (2005) Generalized list T\u2013colorings of cycles. Discrete Appl. Math. 148 (1):13\u201325","DOI":"10.1016\/j.dam.2004.11.005"},{"issue":"8","key":"791_CR7","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.1016\/j.disc.2007.07.075","volume":"308","author":"D Gon\u00e7alves","year":"2008","unstructured":"Gon\u00e7alves D (2008) On the $$L(p,1)$$-labelling of graphs. Disc Math 308(8):1405\u20131414","journal-title":"Disc Math"},{"key":"791_CR8","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1137\/0405048","volume":"5","author":"JR Griggs","year":"1992","unstructured":"Griggs JR, Yeh RK (1992) Labeling graphs with a condition at distance 2. SIAM J Disc Math 5:586\u2013595","journal-title":"SIAM J Disc Math"},{"issue":"12","key":"791_CR9","doi-asserted-by":"publisher","first-page":"1497","DOI":"10.1109\/PROC.1980.11899","volume":"68","author":"WK Hale","year":"1980","unstructured":"Hale WK (1980) Frequency assignment: theory and applications. Proc IEEE 68(12):1497\u20131514","journal-title":"Proc IEEE"},{"key":"791_CR10","doi-asserted-by":"crossref","unstructured":"Havet F, Reed B, Sereni JS (2012) Griggs and Yeh\u2019s conjecture and L(p,1) \u2013labellings. SIAM J Discrete Math 26(1):145\u2013168","DOI":"10.1137\/090763998"},{"key":"791_CR11","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s00373-017-1760-0","volume":"33","author":"JJ Huo","year":"2017","unstructured":"Huo JJ, Wang WF, Xu CD (2017) Neighbor sum distinguishing index of subcubic graphs. Graphs Comb 33:419\u2013431","journal-title":"Graphs Comb"},{"issue":"3","key":"791_CR12","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1137\/S0895480101399449","volume":"16","author":"D Kr\u00e1l","year":"2003","unstructured":"Kr\u00e1l D, \u0160krekovski R (2003) A theorem about channel assignment problem. SIAM J Disc Math 16(3):426\u2013437","journal-title":"SIAM J Disc Math"},{"key":"791_CR13","doi-asserted-by":"crossref","unstructured":"Molloy M, Salavatipour MR (2005) A bound on the chromatic number of the square of a planar graph. J Comb Theory Ser B 94(2): 189\u2013213","DOI":"10.1016\/j.jctb.2004.12.005"},{"key":"791_CR14","doi-asserted-by":"crossref","unstructured":"Van den Heuvel J, McGuinness S (2003) Coloring of the square of a planar graph. J Graph Theory 42:110\u2013124","DOI":"10.1002\/jgt.10077"},{"key":"791_CR15","doi-asserted-by":"publisher","first-page":"598","DOI":"10.1016\/j.dam.2005.09.007","volume":"154","author":"WF Wang","year":"2006","unstructured":"Wang WF (2006) The L(2,1)-labelling of trees. Disc Appl Math 154:598\u2013603","journal-title":"Disc Appl Math"},{"key":"791_CR16","doi-asserted-by":"publisher","first-page":"2241","DOI":"10.1016\/j.dam.2007.05.061","volume":"156","author":"WF Wang","year":"2008","unstructured":"Wang WF, Cai LZ (2008) Labelling planar graphs without 4-cycles with a conditionon distance two. Disc Appl Math 156:2241\u20132249","journal-title":"Disc Appl Math"},{"key":"791_CR17","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1137\/S0895480101390448","volume":"17","author":"WF Wang","year":"2003","unstructured":"Wang WF, Lih KW (2003) Labeling planar graphs with conditions on girth and distance two. SIAM J Disc Math 17:264\u2013275","journal-title":"SIAM J Disc Math"},{"key":"791_CR18","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1137\/10080453X","volume":"26","author":"HY Zhu","year":"2012","unstructured":"Zhu HY, Lv XZ, Wang CQ, Chen M (2012) Labelling planar graphs without 4,5-cycles with a condition on distance two. SIAM J Disc Math 26:52\u201364","journal-title":"SIAM J Disc Math"},{"key":"791_CR19","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/j.dam.2013.08.039","volume":"162","author":"HY Zhu","year":"2014","unstructured":"Zhu HY, Hou LF, Chen W, Lv XZ (2014) The $$L(p, q)$$-labelling of planar graphs without 4-cycles. Disc Appl Math 162:355\u2013363","journal-title":"Disc Appl Math"},{"key":"791_CR20","doi-asserted-by":"publisher","first-page":"2211","DOI":"10.1016\/j.disc.2018.04.025","volume":"341","author":"HY Zhu","year":"2018","unstructured":"Zhu HY, Miao LY, Chen S, Lv XZ, Song WY (2018) The list $$L(2,1)$$-labeling of planar graphs. Disc Math 341:2211\u20132219","journal-title":"Disc Math"},{"key":"791_CR21","doi-asserted-by":"publisher","first-page":"1411","DOI":"10.1007\/s10878-018-0312-8","volume":"36","author":"HY Zhu","year":"2018","unstructured":"Zhu HY, Gu Y, Sheng JJ, Lv XZ (2018) List 2-distance $$\\Delta +3$$-coloring of planar graphs without 4,5-cycles. J Comb Optim 36:1411\u20131424","journal-title":"J Comb Optim"},{"key":"791_CR22","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1007\/s10898-018-0647-9","volume":"72","author":"JL Zhu","year":"2018","unstructured":"Zhu JL, Bu YH, Pardalos MP, Du HW, Wang HJ, Liu B (2018) Optimal channel assignment and $$L(p,1)$$-labeling. J Global Optim 72:539\u2013552","journal-title":"J Global Optim"},{"key":"791_CR23","doi-asserted-by":"crossref","unstructured":"Zhu HY, Zhu JL, Liu Y, Wang SL, Huang DJ, Miao LY (2020) The list L(2,1) \u2013labeing of planar graps with large girth, In: Zhang Z, Li W, Du DZ (eds) Algorithmic applications in management AAIM 2020: lecture notes in computer science, 12290, pp 501\u2013512","DOI":"10.1007\/978-3-030-57602-8_45"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-021-00791-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-021-00791-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-021-00791-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T20:21:49Z","timestamp":1665778909000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-021-00791-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,11]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["791"],"URL":"https:\/\/doi.org\/10.1007\/s10878-021-00791-5","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"value":"1382-6905","type":"print"},{"value":"1573-2886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,11]]},"assertion":[{"value":"19 July 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 August 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}