{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:43:36Z","timestamp":1760150616533,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,22]],"date-time":"2023-12-22T00:00:00Z","timestamp":1703203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12131013"],"award-info":[{"award-number":["12131013"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper introduces the forbidden subgraph conditions for Hamilton-connected graphs. If the degree sequence of the graph is (4,2,2,2,2) and it is connected, then it is called hourglass\u03930. For integers i\u22651, the graph Zi is paw, which is obtained by attaching one of the vertices of the triangle to one of the end vertices of a path with a number of edges i. We show that every graph G is Hamilton-connected if G is a \u03930-free, K1,3-free, Z14-free, and a 3-connected graph. Moreover, we give an example to show the sharpness of a paw-type forbidden subgraph in a 3-connected, Hamilton-connected graph. Our focus on the Hamilton-connected problem can be applied to data center networks (DCNs). In the future, we will remove the forbidden subgraph families from our conclusions when building the network to obtain the optimal communication cost. Our result extends the result of Ryj\u00e1\u010dek and Vr\u00e1na (Discrete Mathematics 344: 112350, 2021).<\/jats:p>","DOI":"10.3390\/axioms13010010","type":"journal-article","created":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T20:42:30Z","timestamp":1703450550000},"page":"10","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Paw-Type Characterization of Hourglass-Free Hamilton-Connected Graphs"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6664-2546","authenticated-orcid":false,"given":"Panpan","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3091-3252","authenticated-orcid":false,"given":"Liming","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bondy, J.A., and Murty, U.S.R. (2008). Graph Theory, Springer.","DOI":"10.1007\/978-1-84628-970-5"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"112350","DOI":"10.1016\/j.disc.2021.112350","article-title":"Every 3-connected {K1,3,Z7}-free graph of order at least 21 is Hamilton-connected","volume":"344","year":"2021","journal-title":"Discret. 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Designing 2D and 3D Network-on-Chip Architectures, Springer.","DOI":"10.1007\/978-1-4614-4274-5"},{"key":"ref_13","first-page":"152","article-title":"Hamiltonian connectedness in 3-connected line graphs","volume":"157","author":"Lai","year":"2009","journal-title":"Discret. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1016\/j.disc.2018.02.008","article-title":"Degree sum and Hamiltonian-connected line graphs","volume":"341","author":"Lui","year":"2018","journal-title":"Discret. Math."},{"key":"ref_15","unstructured":"Shao, Y. (2005). Claw-Free Graphs and Line Graphs. [Ph.D. Thesis, West Virginia University]."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/1\/10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:40:46Z","timestamp":1760132446000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/1\/10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,22]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["axioms13010010"],"URL":"https:\/\/doi.org\/10.3390\/axioms13010010","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,12,22]]}}}