Hamilton-Connected Mycielski Graphs∗
Jarnicki, Myrvold, Saltzman, and Wagon conjectured that if G is Hamilton-connected and not K2, then its Mycielski graph μG is Hamilton-connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs G with δG>VG/2, generalized Petersen graphs GPn,2 and GP...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/3376981 |
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| _version_ | 1832556629122351104 |
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| author | Yuanyuan Shen Xinhui An Baonyindureng Wu |
| author_facet | Yuanyuan Shen Xinhui An Baonyindureng Wu |
| author_sort | Yuanyuan Shen |
| collection | DOAJ |
| description | Jarnicki, Myrvold, Saltzman, and Wagon conjectured that if G is Hamilton-connected and not K2, then its Mycielski graph μG is Hamilton-connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs G with δG>VG/2, generalized Petersen graphs GPn,2 and GPn,3, and the cubes G3. In addition, if G is pancyclic, then μG is pancyclic. |
| format | Article |
| id | doaj-art-acafead4806e44fc8fb87ec310ceb933 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-acafead4806e44fc8fb87ec310ceb9332025-02-03T05:44:48ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/33769813376981Hamilton-Connected Mycielski Graphs∗Yuanyuan Shen0Xinhui An1Baonyindureng Wu2College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaJarnicki, Myrvold, Saltzman, and Wagon conjectured that if G is Hamilton-connected and not K2, then its Mycielski graph μG is Hamilton-connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs G with δG>VG/2, generalized Petersen graphs GPn,2 and GPn,3, and the cubes G3. In addition, if G is pancyclic, then μG is pancyclic.http://dx.doi.org/10.1155/2021/3376981 |
| spellingShingle | Yuanyuan Shen Xinhui An Baonyindureng Wu Hamilton-Connected Mycielski Graphs∗ Discrete Dynamics in Nature and Society |
| title | Hamilton-Connected Mycielski Graphs∗ |
| title_full | Hamilton-Connected Mycielski Graphs∗ |
| title_fullStr | Hamilton-Connected Mycielski Graphs∗ |
| title_full_unstemmed | Hamilton-Connected Mycielski Graphs∗ |
| title_short | Hamilton-Connected Mycielski Graphs∗ |
| title_sort | hamilton connected mycielski graphs∗ |
| url | http://dx.doi.org/10.1155/2021/3376981 |
| work_keys_str_mv | AT yuanyuanshen hamiltonconnectedmycielskigraphs AT xinhuian hamiltonconnectedmycielskigraphs AT baonyindurengwu hamiltonconnectedmycielskigraphs |