{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T07:04:18Z","timestamp":1770966258135,"version":"3.50.1"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T00:00:00Z","timestamp":1765756800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T00:00:00Z","timestamp":1765756800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12301455"],"award-info":[{"award-number":["12301455"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2023QA080"],"award-info":[{"award-number":["ZR2023QA080"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2024MA073"],"award-info":[{"award-number":["ZR2024MA073"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s00373-025-03002-8","type":"journal-article","created":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T18:54:35Z","timestamp":1765824875000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Note on the 4-Connected Line Graph of a Planar Triangulation Containing Two CISTs"],"prefix":"10.1007","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4085-4524","authenticated-orcid":false,"given":"Maoqun","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruhua","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,12,15]]},"reference":[{"key":"3002_CR1","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1002\/jgt.21780","volume":"77","author":"T Araki","year":"2014","unstructured":"Araki, T.: Dirac\u2019s condition for completely independent spanning trees. J. Graph Theory 77, 171\u2013179 (2014)","journal-title":"J. Graph Theory"},{"key":"3002_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2","volume-title":"Graph Theory with Applications","author":"JA Bondy","year":"1976","unstructured":"Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. NorthHolland, Amsterdam (1976)"},{"key":"3002_CR3","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1109\/TPDS.2020.3029654","volume":"32","author":"G Chen","year":"2021","unstructured":"Chen, G., Cheng, B., Wang, D.: Constructing completely independent spanning trees in data center network based on augmented cube. IEEE Trans. Parallel Distrib. Syst. 32, 665\u2013673 (2021)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"3002_CR4","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/j.tcs.2020.12.023","volume":"856","author":"YH Chang","year":"2021","unstructured":"Chang, Y.H., Pai, K.J., Hsu, C.C., Yang, J.S., Chang, J.M.: Constructing dual-CISTs of folded divide-and-swap cubes. Theor. Comput. Sci. 856, 75\u201387 (2021)","journal-title":"Theor. Comput. Sci."},{"key":"3002_CR5","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.dam.2014.06.002","volume":"177","author":"G Fan","year":"2014","unstructured":"Fan, G., Hong, Y., Liu, Q.: Ore\u2019s condition for completely independent spanning trees. Discrete Appl. Math. 177, 95\u2013100 (2014)","journal-title":"Discrete Appl. Math."},{"key":"3002_CR6","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/S0167-5060(08)70458-8","volume":"41","author":"H Fleischner","year":"1988","unstructured":"Fleischner, H., Jackson, B.: A note concerning some conjectures on cyclically 4-edge connected 3-regular graphs. Ann. Discrete Math. 41, 171\u2013177 (1988)","journal-title":"Ann. Discrete Math."},{"key":"3002_CR7","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/S0012-365X(00)00377-0","volume":"234","author":"T Hasunuma","year":"2001","unstructured":"Hasunuma, T.: Completely independent spanning trees in the underlying graph of a line digraph. Discrete Math. 234, 149\u2013157 (2001)","journal-title":"Discrete Math."},{"key":"3002_CR8","doi-asserted-by":"crossref","unstructured":"Hasunuma, T.: Completely independent spanning trees in maximal planar graphs. in: Graph-Theoretic Concepts in Computer Scrience. in: Lecture Notes in Comput. Sci., Springer, Berlin 235\u2013245 (2002)","DOI":"10.1007\/3-540-36379-3_21"},{"key":"3002_CR9","doi-asserted-by":"crossref","unstructured":"Hasunuma, T.: Minimum degree conditions and optimal graphs for completely independent spanning trees. Proc. 26th International Workshop on Combinatorial Algorithms (IWOCA2015), Lecture Notes in Comput. Sci. Springer, New York 9538, 260\u2013273 (2016)","DOI":"10.1007\/978-3-319-29516-9_22"},{"key":"3002_CR10","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1007\/s00373-023-02688-y","volume":"39","author":"T Hasunuma","year":"2023","unstructured":"Hasunuma, T.: Completely independent spanning trees in line graphs. Graphs Conbin. 39, 90 (2023)","journal-title":"Graphs Conbin."},{"key":"3002_CR11","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1016\/j.ipl.2016.05.004","volume":"116","author":"X Hong","year":"2016","unstructured":"Hong, X., Liu, Q.H.: Degree condition for completely independent spanning trees. Inform. Process. Lett. 116, 644\u2013648 (2016)","journal-title":"Inform. Process. Lett."},{"key":"3002_CR12","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1080\/09728600.2024.2333397","volume":"21","author":"RJ Kingan","year":"2024","unstructured":"Kingan, R.J., Kingan, S.R.: On cyclically 4-connected cubic graphs. AKCE Int. J. Graphs Combin. 21, 255\u2013260 (2024)","journal-title":"AKCE Int. J. Graphs Combin."},{"key":"3002_CR13","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/BF02986673","volume":"10","author":"HJ Lai","year":"1994","unstructured":"Lai, H.J.: Every 4-connected line graph of a planar graph is hamiltonian. Graph Combin. 10, 249\u2013253 (1994)","journal-title":"Graph Combin."},{"key":"3002_CR14","doi-asserted-by":"publisher","first-page":"990","DOI":"10.1007\/s11227-020-03297-9","volume":"77","author":"KJ Pai","year":"2021","unstructured":"Pai, K.J., Chang, R.S., Chang, J.M.: Constructing dual-CISTs of pancake graphs and performance assessment of protection routings on some cayley networks. J. Supercomput. 77, 990\u20131014 (2021)","journal-title":"J. Supercomput."},{"key":"3002_CR15","doi-asserted-by":"publisher","first-page":"932","DOI":"10.1109\/TNSE.2022.3140329","volume":"9","author":"KJ Pai","year":"2022","unstructured":"Pai, K.J., Yang, J.S., Chen, G.Y., Chang, J.M.: Configuring protection routing via completely independent spanning trees in dense gaussian on-chip networks. IEEE Trans. Netw. Sci. Eng. 9, 932\u2013946 (2022)","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"3002_CR16","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1090\/S0002-9947-1956-0081471-8","volume":"82","author":"WT Tutte","year":"1956","unstructured":"Tutte, W.T.: A theorem on planar graphs. Amer. Math. Soc. 82, 99\u2013116 (1956)","journal-title":"Amer. Math. Soc."},{"key":"3002_CR17","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1002\/jgt.3190100308","volume":"10","author":"C Thomassen","year":"1986","unstructured":"Thomassen, C.: Reflections on graph theory. J. Graph Theory 10, 309\u2013324 (1986)","journal-title":"J. Graph Theory"},{"key":"3002_CR18","doi-asserted-by":"publisher","first-page":"378","DOI":"10.2307\/1968197","volume":"32","author":"H Whitney","year":"1931","unstructured":"Whitney, H.: A theorem on graphs. Ann. Math. 32, 378\u2013390 (1931)","journal-title":"Ann. Math."}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-03002-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-025-03002-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-03002-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T06:04:51Z","timestamp":1770962691000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-025-03002-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,15]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["3002"],"URL":"https:\/\/doi.org\/10.1007\/s00373-025-03002-8","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"value":"0911-0119","type":"print"},{"value":"1435-5914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,15]]},"assertion":[{"value":"8 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 December 2025","order":3,"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"}},{"value":"The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Use of AI tools declaration"}}],"article-number":"5"}}