{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T09:40:06Z","timestamp":1748857206205,"version":"3.41.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,4,27]],"date-time":"2025-04-27T00:00:00Z","timestamp":1745712000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,27]],"date-time":"2025-04-27T00:00:00Z","timestamp":1745712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s00373-025-02924-7","type":"journal-article","created":{"date-parts":[[2025,4,27]],"date-time":"2025-04-27T13:03:09Z","timestamp":1745758989000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Hamilton Paths in Vertex-Transitive Graphs of Order 10p"],"prefix":"10.1007","volume":"41","author":[{"given":"Shaofei","family":"Du","sequence":"first","affiliation":[]},{"given":"Wenjuan","family":"Luo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5271-576X","authenticated-orcid":false,"given":"Hao","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,27]]},"reference":[{"key":"2924_CR1","doi-asserted-by":"crossref","unstructured":"Alspach, B.: The search for long paths and cycles in vertex-transitive graphs and digraphs. In: McAvaney, Kevin L. (ed.) Combinatorial Mathematics Vlll. Lecture Notes in Mathematics, vol. 884, pp. 14\u201322. Springer, Berlin (1981)","DOI":"10.1007\/BFb0091804"},{"key":"2924_CR2","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/0012-365X(89)90157-X","volume":"78","author":"B Alspach","year":"1989","unstructured":"Alspach, B.: Lifting Hamilton cycles of quotient graphs. Discrete Math. 78, 25\u201336 (1989)","journal-title":"Discrete Math."},{"key":"2924_CR3","doi-asserted-by":"crossref","unstructured":"Cameron P.J.: (ed.), Problems from the Fifteenth British Combinatorial Conference, Discrete Math. 167\/168, 605\u2013615 (1997)","DOI":"10.1016\/S0012-365X(96)00212-9"},{"key":"2924_CR4","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1112\/S0024610702003484","volume":"66","author":"PJ Cameron","year":"2002","unstructured":"Cameron, P.J., Giudici, M., Jones, G.A., Kantor, W.M., Klin, M.H., Maru\u0161i\u010d, D., Nowitz, L.A.: Transitive permutation groups without semiregular subgroups. J. Lond. Math. Soc. 66, 325\u2013333 (2002)","journal-title":"J. Lond. Math. Soc."},{"key":"2924_CR5","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1006\/jctb.1997.1796","volume":"72","author":"YQ Chen","year":"1998","unstructured":"Chen, Y.Q.: On Hamiltonicity of vertex-transitive graphs and digraphs of order $$p^4$$. J. Combin. Theory Ser. B 72, 110\u2013121 (1998)","journal-title":"J. Combin. Theory Ser. B"},{"key":"2924_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0012-365X(95)00072-5","volume":"156","author":"S Curran","year":"1996","unstructured":"Curran, S., Gallian, J.A.: Hamiltonian cycles and paths in Cayley graphs and digraphs - a survey. Discrete Math. 156, 1\u201318 (1996)","journal-title":"Discrete Math."},{"key":"2924_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.26493\/1855-3974.2163.5df","volume":"19","author":"SF Du","year":"2020","unstructured":"Du, S.F., Kutnar, K., Maru\u0161i\u010d, D.: Hamilton cycles in primeitive vertex-transitive graphs of a product of two primes\u2013the case $${\\rm PSL}(2, q^2)$$ acting on cosets of $${\\rm PSL}(2, q)$$. Ars Math. Contemp. 19, 1\u201315 (2020)","journal-title":"Ars Math. Contemp."},{"key":"2924_CR8","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/s00493-020-4384-6","volume":"41","author":"SF Du","year":"2021","unstructured":"Du, S.F., Kutnar, K., Maru\u0161i\u010d, D.: Resolving the Hamiltonian problem for vertex-transitive graphs of order a product of two primes. Combinatorica 41, 507\u2013543 (2021)","journal-title":"Combinatorica"},{"key":"2924_CR9","doi-asserted-by":"crossref","unstructured":"Du, S.F., Tian, Y., Yu, H.: Hamilton cycles in primitive graphs of order $$2rs$$. Ars Math. Contemp. 23, Paper No. 5, 24 pp (2023)","DOI":"10.26493\/1855-3974.2930.8e4"},{"key":"2924_CR10","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1016\/j.jctb.2006.06.004","volume":"97","author":"E Dobson","year":"2007","unstructured":"Dobson, E., Malni\u010d, A., Maru\u0161i\u010d, D., Nowitz, L.A.: Semiregular automorphisms of vertex-transitive graphs of certain valencies. J. Combin. Theory Ser. B 97, 371\u2013380 (2007)","journal-title":"J. Combin. Theory Ser. B"},{"key":"2924_CR11","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/0012-365X(83)90270-4","volume":"46","author":"E Durnberger","year":"1983","unstructured":"Durnberger, E.: Connected Cayley graphs of semi-direct products of cyclic groups of prime order by abelian groups are hamiltonian. Discrete Math. 46, 55\u201368 (1983)","journal-title":"Discrete Math."},{"key":"2924_CR12","first-page":"55","volume":"7","author":"E Ghaderpour","year":"2014","unstructured":"Ghaderpour, E., Witte Morris, D.: Cayley graphs on nilpotent groups with cyclic commutator subgroup are hamiltonian, Ars Math. Contemp. 7, 55\u201372 (2014)","journal-title":"Contemp."},{"key":"2924_CR13","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1112\/S0024610702003812","volume":"67","author":"M Giudici","year":"2003","unstructured":"Giudici, M.: Quasiprimitive groups with no fixed point free elements of prime order. J. Lond. Math. Soc. 67, 73\u201384 (2003)","journal-title":"J. Lond. Math. Soc."},{"key":"2924_CR14","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1112\/plms\/pdr042","volume":"104","author":"HH Glover","year":"2012","unstructured":"Glover, H.H., Kutnar, K., Malni\u010d, A., Maru\u0161i\u010d, D.: Hamilton cycles in $$(2, odd,3)$$-Cayley graphs. Proc. Lond. Math. Soc. 104, 1171\u20131197 (2012)","journal-title":"Proc. Lond. Math. Soc."},{"key":"2924_CR15","doi-asserted-by":"publisher","first-page":"775","DOI":"10.4171\/jems\/96","volume":"9","author":"HH Glover","year":"2007","unstructured":"Glover, H.H., Maru\u0161i\u010d, D.: Hamiltonicity of cubic Cayley graph. J. Eur. Math. Soc. 9, 775\u2013787 (2007)","journal-title":"J. Eur. Math. Soc."},{"key":"2924_CR16","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1016\/j.ejc.2007.02.002","volume":"29","author":"K Kutnar","year":"2008","unstructured":"Kutnar, K., Maru\u0161i\u010d, D.: Hamiltonicity of vertex-transitive graphs of order $$4p$$. Eur. J. Combin. 29, 423\u2013438 (2008)","journal-title":"Eur. J. Combin."},{"key":"2924_CR17","doi-asserted-by":"publisher","first-page":"5491","DOI":"10.1016\/j.disc.2009.02.017","volume":"309","author":"K Kutnar","year":"2009","unstructured":"Kutnar, K., Maru\u0161i\u010d, D.: Hamilton cycles and paths in vertex-transitive graphs - Current directions. Discrete Math. 309, 5491\u20135500 (2009)","journal-title":"Discrete Math."},{"key":"2924_CR18","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1016\/j.ejc.2012.01.005","volume":"33","author":"K Kutnar","year":"2012","unstructured":"Kutnar, K., Maru\u0161i\u010d, D., Zhang, C.: Hamilton paths in vertex-transitive graphs of order $$10p$$. Eur. J. Combin. 33, 1043\u20131077 (2012)","journal-title":"Eur. J. Combin."},{"key":"2924_CR19","doi-asserted-by":"publisher","first-page":"5444","DOI":"10.1016\/j.disc.2008.12.005","volume":"309","author":"K Kutnar","year":"2009","unstructured":"Kutnar, K., \u0160parl, P.: Hamilton paths and cycles in vertex-transitive graphs of order $$6p$$. Discrete Math. 309, 5444\u20135460 (2009)","journal-title":"Discrete Math."},{"key":"2924_CR20","volume-title":"Finite Fields","author":"R Lidl","year":"1997","unstructured":"Lidl, R., Niederreiter, H.: Finite Fields. Cambridge University Press, Cambridge (1997)"},{"key":"2924_CR21","unstructured":"Lov\u00e1sz, L.: Combinatorial Structures and Their Applications. In: Guy, R., Hanam, H., Sauer, N., Schonheim, J. (Eds.) Gordon and Breach, New York (1970)"},{"key":"2924_CR22","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/0012-365X(81)90174-6","volume":"36","author":"D Maru\u0161i\u010d","year":"1981","unstructured":"Maru\u0161i\u010d, D.: On vertex symmetric digraphs. Discrete Math. 36, 69\u201381 (1981)","journal-title":"Discrete Math."},{"key":"2924_CR23","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/0012-365X(83)90269-8","volume":"46","author":"D Maru\u0161i\u010d","year":"1983","unstructured":"Maru\u0161i\u010d, D.: Hamiltonian circuits in Cayley graphs. Discrete Math. 46, 49\u201354 (1983)","journal-title":"Discrete Math."},{"key":"2924_CR24","doi-asserted-by":"crossref","unstructured":"Maru\u0161i\u010d, D.: Vertex transitive graphs and digraphs of order $$p^k$$, Cycles in graphs (Burnaby, B.C., 1982) 115\u2013128. Ann. Discrete Math. 27, North-Holland, Amsterdam (1985)","DOI":"10.1016\/S0304-0208(08)73001-9"},{"key":"2924_CR25","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/0012-365X(87)90129-4","volume":"66","author":"D Maru\u0161i\u010d","year":"1987","unstructured":"Maru\u0161i\u010d, D.: Hamiltonian cycles in vertex symmetric graphs of order $$2p^2$$. Discrete Math. 66, 169\u2013174 (1987)","journal-title":"Discrete Math."},{"key":"2924_CR26","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1016\/0012-365X(82)90220-5","volume":"42","author":"D Maru\u0161i\u010d","year":"1982","unstructured":"Maru\u0161i\u010d, D., Parsons, T.D.: Hamiltonian paths in vertex-symmetric graphs of order $$5p$$. Discrete Math. 42, 227\u2013242 (1982)","journal-title":"Discrete Math."},{"key":"2924_CR27","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/0012-365X(83)90024-9","volume":"43","author":"D Maru\u0161i\u010d","year":"1983","unstructured":"Maru\u0161i\u010d, D., Parsons, T.D.: Hamiltonian paths in vertex-symmetric graphs of order $$4p$$. Discrete Math. 43, 91\u201396 (1983)","journal-title":"Discrete Math."},{"key":"2924_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.26493\/1855-3974.330.0e6","volume":"8","author":"D Witte Morris","year":"2015","unstructured":"Witte Morris, D.: Odd-order Cayley graphs with commutator subgroup of order $$pq$$ are hamiltonian. Ars. Math. Contemp. 8, 1\u201328 (2015)","journal-title":"Ars. Math. Contemp."},{"key":"2924_CR29","doi-asserted-by":"crossref","unstructured":"Witte Morris, D.: Cayley graphs on groups with commutator subgroup of order $$2p$$ are hamiltonian. Art Discrete Appl. Math. 1, $$\\#$$P1.04 (2018)","DOI":"10.26493\/2590-9770.1240.60e"},{"key":"2924_CR30","doi-asserted-by":"crossref","unstructured":"Zhang, J.Y.: Vertex-transitive digraphs of order $$p^5$$ are Hamiltonian. Electron. J. Combin. 22, $$\\#$$P1.76 (2015)","DOI":"10.37236\/4034"}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-02924-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-025-02924-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-02924-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T09:15:40Z","timestamp":1748855740000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-025-02924-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,27]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["2924"],"URL":"https:\/\/doi.org\/10.1007\/s00373-025-02924-7","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"type":"print","value":"0911-0119"},{"type":"electronic","value":"1435-5914"}],"subject":[],"published":{"date-parts":[[2025,4,27]]},"assertion":[{"value":"6 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 April 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 have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}],"article-number":"66"}}